Response to Competitive Entry: A Rationale for Delayed

Marketing Science/Vol. 17, No. 4, 1998

pp. 380–405

0732-2399/98/1704/0380$05.00Copyright q 1998, Institute for Operations Research

and the Management Sciences

Response to Competitive Entry: A Rationalefor Delayed Defensive Reaction

Ajay Kalra • Surendra Rajiv • Kannan SrinivasanGraduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890

Graduate School of Business, University of Chicago, Chicago, Illinois 60637Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890

[email protected]

AbstractEmpirical studies examining responses to new product en-tries come to the puzzling conclusion that, in general, an in-cumbent reacts to a new entrant after a significant delay.Even easy-to-implement price cuts are observed after signifi-cant lag following entry. These findings seem to contradictthe existing literature that either implicitly assumes orstrongly advocates immediate defensive responses to limitcompetitive encroachment. When a competing firm entersthe market, consumers may be uncertain about the enteringfirm’s product quality. The incumbent firm (through rigor-ous tests) may fully know the entrant’s quality. Suppose theincumbent aggressively lowers price. This may cause theconsumers to wonder if indeed the entrant’s quality is high.In other words, an incumbent’s reaction may cause the con-sumers to make inferences about the entrant’s quality. Suchstrategic implications of the incumbent’s reactions have to becarefully analyzed before determining the optimal responseby the incumbent.

In this paper, we propose a conceptual framework for un-derstanding differences in the magnitude and timing of in-cumbents’ responses to competitive entries. We consider amodel in which a monopolist incumbent firm faces compet-itive entry. The incumbent firm knows the true quality of theentrant with certainty. Although consumers are aware of theincumbent’s product quality through their prior experience,they are initially uncertain of the entrant’s product quality.In such a situation, a high-quality entrant has the incentiveto signal her true quality through her strategic price choice.However, the uncertainty about the entrant’s quality is fa-vorable to the incumbent in the sense that consumers believewith a high probability that the entrant’s quality is low. Asa result, the strategic incentives facing the incumbent and theentrant oppose each other. While the entrant wants to signalher high quality, the incumbent wants to prevent her fromdoing so. We demonstrate that one way the incumbent canprevent the quality signaling is to select a higher than hisoptimal competitive (duopoly) price. In other words, the in-cumbent can prevent or “jam” the entrant’s quality signalingby choosing a price higher than his optimal competitive pricewhen consumers are fully informed about the entrant’s true

quality. Though the signal-jamming price is lower than themonopoly price, the price is substantially higher than thecompetitive price. This marginal reduction in the incum-bent’s price from the pre-entry monopolistic price representsa muted or lack of response by the incumbent to the com-petitive entry. However, once the entrant’s quality gets re-vealed in subsequent periods through consumer usage andword of mouth, the entrant has no incentive to engage inquality signaling and the incumbent has no incentive to jamit. Therefore, the market reverts to the complete-informationcompetitive prices, and the incumbent lowers his price con-siderably. This temporal pattern of muted price reduction inthe first period followed by a sharp price reduction in thesecond period corresponds to a delayed defensive reactionin our model. Although the empirical studies suggest thatthe delayed reaction may arise due to factors such as man-agerial inertia or indecision, we demonstrate that such a be-havior is indeed an optimal strategy for a profit-maximizingfirm. Thus, our model reconciles empirical results with theequilibrium outcome of a strategic analytical framework.

Furthermore, in an experimental setting, we test the pre-dictive power of our framework and establish that consum-ers indeed form conjectures about the entrant’s quality basedon the incumbent’s reactions. In the first experimental study,we find strong support for the notion that the incumbent’sprice reaction may indicate entrant’s quality. In a follow-upstudy, we observe that whenever the incumbent lowersprices, respondents judge the quality of the entrant to behigher as compared to the case when prices are the same orincreased. The managerial implication of this paper is thatwell-established incumbent firms should be cautious in theimplementation of their defensive responses to product in-troductions of uncertain quality by competitors. Of particularconcern are situations where the reactions are easily observ-able by consumers. A strong reaction may suggest that theincumbent takes the competitive threat seriously, leadingconsumers to believe in the quality of the competitor’sproduct.(New Product Entry; Defensive Reaction; Quality Signaling;Price-Quality Relationship; Signal Jamming; AsymmetricInformation)

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RESPONSE TO COMPETITIVE ENTRY: A RATIONALE FOR DELAYEDDEFENSIVE REACTION

Marketing Science/Vol. 17, No. 4, 1998 381

1. IntroductionCompetitive reaction to entry has received consider-able attention in the marketing and economics areas.As entry intensifies competition, incumbent firms mustlower prices in response to entry. The following an-ecdotal evidence exemplifies this expectation:

In 1975, Bristol-Myers introduced Datril, an acetaminophen(non-aspirin) analgesic, to the market. The major player in thenonprescription analgesic market then was Tylenol, whichwas produced and marketed by McNeil Labs, a subsidiary ofJohnson and Johnson. Datril was introduced as a low-pricedalternative to Tylenol. Two weeks before Datril’s introduc-tion, McNeil Labs responded by reducing the price of Tylenolto the trade by 30%. In addition, in 1975, McNeil Labs in-creased their advertising budget to promote Tylenol from anestimated $2 million in 1974 to $8 million.

Observe that the incumbent, which was the dominantfirm in the pre-entry period, responded to the newcompetitive threat immediately. Interestingly, how-ever, incumbents often do not respond immediately.Consider the following anecdote that buttresses thispoint:

Gatorade, introduced in 1966, is the major player in the sportsdrink market. In 1991, it held a 86.6% market share (BeverageWorld 1992). The first set of competitors included Suntory Wa-ter Group’s 10-K, which entered in 1986, Powerburst in 1989,and Pepsi’s Mountain Dew Sport (later changed to All Sport)in 1990 (Supermarket News 1990). Despite these new entrantsthat were lower priced, Gatorade maintained high price lev-els. In 1990 Coca-Cola introduced PowerAde nationwidethrough fountains and subsequently in cans and bottles. Thedefensive response to the new competitors was made in 1993when Gatorade engaged in price wars with PowerAde(BrandWeek July 12, 1993).

Surprisingly, this delayed reaction is not an isolatedexample and, in fact, is a widely observed strategy. Ina study based on the Strategic Planning Institute’s (SPI)start-up business data pertaining to 199 new productentries, Robinson (1988) observed a pattern of delayedresponses by the incumbent firms. In particular, defen-sive price reactions, which are the easiest to imple-ment, are also often delayed. Similarly, Bowman andGatignon (1995) also observed delayed responses inthe PIMS database. They note that in 28.7% of thecases, the defensive responses to new product entriesoccurred after more than a year; in 18% of the cases, itoccurred between six months and a year; and in only

13.4% of the cases was there an immediate defensiveresponse. Given such contrasting patterns of defensiveresponse by the incumbent, the following questionsnaturally arise: Why do some incumbents choose torespond immediately to the competitive threat whileothers elect to delay their responses? What are the in-stitutional features and strategic considerations thatprompt incumbents to delay their defensive reactions?We set out to examine these issues here.

Economic theory would suggest that competitive re-sponses occur because, in the pre-entry period, the in-cumbent is a de facto monopolist and hence sets mo-nopoly profit-maximizing prices. However, after thenew product entry, the market structure changes to amore competitive situation that leads an incumbentfirm to reduce his price so as to limit competitive en-croachment. This observed pattern of decrease in theincumbent’s prices in the post-entry period relative tothe pre-entry period can be conceptualized as defensiveresponse by the incumbent.

1.1. A Brief Overview of the Model, Main Results,and Intuition

We consider a stylized model in which there is an in-cumbent firm that faces competitive entry.1 Consumersin the market are aware of the incumbent’s quality byvirtue of buying its product in the past. However, theyare uncertain of the entrant’s quality. (The literatureon pioneering advantage suggests the uncertainty re-lated to the later entrant’s quality as a rationale forfirst-mover advantage; see Schmalensee (1978) andRobinson and Fornell (1985) for additional insights.) Incontrast, the incumbent through reverse engineeringand market research, can correctly gauge the qualityof the entrant. Clearly, such a strategy is too costly forany individual customer.

What should the entrant do when consumers are un-certain of her2 quality? For exposition, consumer un-certainty can be thought of as if the consumers werefacing either a low-quality entrant or a high-quality

1Our focus is on the nature of price competition in the post-entryperiod. Thus, we abstract away from strategic considerations facingthe incumbent in the pre-entry period such as entry deterrence andlimit pricing (Milgrom and Roberts 1982; Srinivasan 1991).2For ease of exposition, we refer to the incumbent as “he” and theentrant as “she.”

KALRA, RAJIV, AND SRINIVASANResponse to Competitive Entry

382 Marketing Science/Vol. 17, No. 4, 1998

entrant, but they are not sure. The credible signalingstrategy of the high-quality entrant is to separate her-self from a possible “ghost” low-quality entrant. Es-sentially, the high-quality entrant must select a strat-egy such that it is too costly for any low-cost entrantto select the same strategy to imitate and hide her lowquality. (In fact, the low-quality entrant prefers to se-lect an optimal strategy, even if her low quality is re-vealed, rather than imitate.) When such different strat-egies would be adopted by the high- and low-qualityentrants, consumers, on observing the entrant’s strat-egy, must correctly infer whether the entrant quality ishigh or low. The literature in the quality-signaling areasuggests that a high-quality entrant should raise pricesto signal higher quality (Bagwell and Riordan 1991;Milgrom and Roberts 1986). The reasoning is that if theentrant’s quality and hence cost of production are high,any decrease in volume due to higher prices wouldhurt the low-quality entrant with a lower cost morethan the high-quality entrant. Therefore, at sufficientlyhigh prices, the low-quality incumbent would preferto select a optimal low price and be known as the low-quality entrant instead of imitating the high price toavoid revelation of low quality. Consequently, when ahigh price is observed, consumers must correctly inferthat the entrant’s quality is high.

These signaling strategies have been studied in thecontext of a monopolist firm attempting to inform un-certain consumers. What sets our analysis apart fromthese studies is that we are considering a competitivemarket with an incumbent offering a product ofknown quality. In this context, consider a high-qualityentrant competing with the incumbent and facing un-certain consumers. As before, the entrant would try toselect a high price to signal high quality. Note thatwhile consumer uncertainty is unfavorable for thehigh-quality entrant, it is favorable for the incumbentwho knows the entrant’s high quality. Therefore, theincumbent’s and the entrant’s incentives oppose eachother. While the entrant wants to signal her high qual-ity, the incumbent wants to prevent her from doing so.One way the incumbent can prevent the quality signalis to select higher than optimal duopoly price (that is,higher than duopoly prices that are much lower thanthe monopoly prices). By doing so, the high-qualityentrant is forced to raise prices even higher to signal

quality. More important, as we demonstrate in this pa-per, the efficiency of higher price as a signal decreaseswith increasing price of the incumbent. Consequently,the entrant’s ability to signal declines when the incum-bent raises the price. In fact, the incumbent throughhigher price selection can prevent or “jam” the entrantfrom engaging in quality signaling. We reiterate thatthe duopoly prices are much lower than the monopolyprices. Thus, even when the incumbent selects a higherthan duopoly price to jam the entrant’s signal, his priceis below the monopoly price. This marginal price re-duction represents a muted or lack of price responseto the entry. Once the entrant is in the market place,her quality would get revealed over time as consumersbuy the product and use it. (Note that even when thequality signal is jammed, the entrant achieves positivesales.) After the quality of the entrant is eventuallylearned, the entrant has no incentive to engage in qual-ity signaling and the incumbent has no incentive to jamit. Therefore, the market reverts to the informed duo-polistic competition, and thus the incumbent lowershis price considerably. This temporal pattern of mutedprice reduction in the first period followed by sharpprice reduction in the second period represents theprediction of delayed reaction in our model.

We believe that even to the reader less familiar withthe signaling analysis and logic, our model offers acompelling intuition. At the risk of being somewhatimprecise, when the incumbent aggressively reacts tocompetitive entry by sharply lowering his price, con-sumers may wonder if the entrant’s product is superioror better. This notion constitutes the genesis of ouranalysis. Apart from a rigorous analytical formulationderiving this intuition, we also subject it to experimen-tal tests. The experimental verification is not an elab-orate test of the model; rather, it aims to assess whetherthe central premise of the model has any face validity.In the first experimental study, from a number of com-peting explanations for delayed reaction, respondentschose our intuition as the most important reason. In asecond experiment, we closely examine the underpin-nings of our model explanations. Our results supportthe notion that when the incumbent lowers price, re-spondents expect the entrant’s quality to be high andvice versa.

We recognize that the incumbent, besides pricing,



can utilize other elements of the marketing-mix ele-ments to respond to the competitive threat. For in-stance, in the context of product strategy this couldentail either repositioning the existing products on thequality dimension (Hauser and Shugan 1983) or broad-ening the product line(s) by introducing new products.Such strategic considerations have an intrinsic time di-mension and thus can be considered as delayed reac-tion. Yet it is unclear as to why immediate price reac-tion (that can be modified before responding withother marketing-mix elements) is still not an optimalstrategy.

1.2. Managerial ImplicationsThe genesis of the explanation offered in this paper isa direct outcome of class discussions with executivesfor the Harvard case “Deere & Co.: Industrial Equip-ment Operations.” In this case, Deere enters the marketsegment of heavy bulldozers with claims of superiorquality. The technology behind the product improve-ment is untested and hence there is uncertainty aboutthe reliability of this technology. While identifying thedefensive reactions by the incumbent firm, Caterpillar,several participants are usually concerned about thepotential inference by the contractors (customers)about Deere’s product if Caterpillar lowers the price.Another example also underscores this point. The ag-gressive price and non-price response by Pepsi to anentry by Coke into its segment has led to the conclu-sion, “All the counterattacking by Pepsi legitimized the(Coke) product” (Wall Street Journal 1990).

The timing of competitive response, therefore, hassignificant strategic implications. In the context of ouranalysis, we find that when consumers are uncertainabout the entrant’s quality, the incumbent firm mustbe careful in deciding the optimal response to entry.Given that the incumbent’s ability to test and identifythe quality of a product far exceeds that of any indi-vidual consumer, it is reasonable for consumers to ex-pect that firms are aware of each other’s quality. Anyaggressive attempt by the incumbent firm may lead thecustomers to view the incumbent’s strong defensivereactions as an implicit acknowledgment of the com-petitor’s strength in the marketplace. In fact, such be-liefs may enhance the attractiveness of the competitor’sproduct.

The incumbent’s defensive strategies, given theabove consideration, will vary depending on whetheror not such strategies are easily observable by the con-sumers. For example, price and advertising responsesare more visible to consumers as compared to tradepromotions. Thus, a firm that aims to respond vigor-ously and immediately but does not want consumersto view the entrant’s product favorably may select dis-creet alternatives such as trade promotion and sales-force incentives.

The conceptual framework that we propose and thestrategic considerations impacting on the incumbent’stiming of defensive response that we highlight are ofparticular managerial relevance in those cases whenthe entrant’s reputation for delivering high quality isnonexistent or weak. When a new firm with limited orno prior track record enters a market, the quality un-certainty is likely to exist. Such uncertainty may alsobe prevalent even for established firms when they en-ter new segments or when they adopt new technolo-gies. In these markets, incumbent firms will have toexamine the optimal timing of their defensivereactions.

1.3. Related LiteratureDefensive strategies by incumbent firms to new com-petitive threats have received considerable attention inthe literature. While the literature has focused primar-ily on the direction (Hauser and Shugan 1983), inten-sity (Gatignon, Anderson, and Helsen 1989), and scope(Karnani and Wernerfelt 1985) of the incumbent’s re-sponses, a few empirical studies in marketing have ex-amined the timing of competitive response to newproduct introductions (Bowman and Gatignon 1995;Robinson 1988). As mentioned earlier, the empiricalfindings have indicated a variety of responses and par-ticularly delayed responses by the incumbent firms(Biggadike 1979; Bowman and Gatignon 1995; Chen,Smith, and Grimm 1992; MacMillan, McCaffery, andVan Wijk 1985; Robinson 1988). This empirical findingof delayed response is contradictory to the normativeliterature (Hauser and Shugan 1983; Kumar andSudarshan 1988; Porter 1985) that either implicitly as-sumes immediate response (or is silent on the timingissue) or explicitly advocates immediate responses. For



example, Porter (1985, p. 498) recommends that “as ageneral rule, quick and vigorous retaliation isnecessary.”

The contradiction between the normative modelsand the empirical findings has led to conjectures in theliterature to account for this discrepancy. For instance,Gatignon, Anderson, and Helsen (1989) ascribe thelack of initial reactions by incumbent firms to their “in-ability to respond effectively.” They argue that firmsmay be uncertain about the best way to respond tocompetitive actions or may lack the managerial exper-tise to do so. Extending this argument, Bowman andGatignon (1995) hypothesize that firms operating inrelatively more stable market environments may be in-efficient in processing competitive information andthus delay responses as compared to firms operatingin unstable environments. Though it is plausible thatmanagerial inefficiency or indecision is likely to causedelay in response by the incumbent, it is hard to claimthat all delays are likely to be caused by managerialineptitude or indecisiveness. Another conjecture byBowman and Gatignon (1995) is that an incumbent’sreaction will be faster in a market with a high growthrate. In such rapidly growing markets, possible capac-ity constraints may suggest delayed rather than im-mediate reaction. Also, low growth markets become azero-sum game arena. In these markets, incumbentsmay react immediately to retain their market share.More important, for these conjectures, it is unclear asto why delayed reaction emerges as the optimal strat-egy for a profit-maximizing incumbent.3

In any event, our experimental study provides ameasure of direct comparison of the relative impor-tance of the various explanations. The explanation thatconsumers may infer the entrant’s quality based on theincumbent’s reaction is viewed as the most likely rea-son. While the usual caveats of interpreting experi-mental results are readily applicable, at a minimum,

3In a market where consumers face switching cost (Klemperer 1987),an incumbent firm’s incentive to respond immediately is somewhatmitigated since the switching cost limits the competitive encroach-ment by the entrant. We thank an anonymous reviewer for pointingout this reason. We show that even when switching cost is absent,delayed reaction may be an optimal strategy due to signaling con-siderations.

the finding underscores the importance of the expla-nation developed in this paper.

2. The ModelIn this section, we lay out the model formulation anddiscuss the main assumptions. In § 2.1, we characterizethe consumer behavior assumed in our analysis. In §2.2, we derive the demand functions facing the incum-bent and the entrant.

2.1. Consumer ModelLet qI be the quality of the incumbent’s product and letqE be the quality of the entrant’s product. We assumethat even though all consumers value higher levels ofquality, they are heterogeneous in their willingness topay for incremental quality. We capture this aspect ofconsumer heterogeneity by assuming that the mar-ginal willingness to pay for quality, ], is distributeduniformly over the interval [0,1]. Consumers purchaseat most one unit of the product in any time period.Consumer purchase decision is dictated by the stan-dard utility maximization framework. Thus, a con-sumer will purchase the product (either the incum-bent’s or the entrant’s) whenever the expected value ofthe product exceeds the market price and will selectthe brand (either the incumbent’s or the entrant’s prod-uct) that yields the highest surplus.

As mentioned earlier, we assume that consumersdiffer in their valuation of quality. Let the set of poten-tial consumers correspond to the interval [0,1] with auniform distribution and total mass N. Without anyloss of generality, we normalize the mass of potentialconsumers to be unity, i.e., we set N 4 1. In the fol-lowing analysis, we assume that the net surplus to theconsumer located at h for a good of quality q at pricep is given by u(q, p|h) 4 hq 1 p. This specification ofconsumer surplus function is similar to those used inMilgrom and Roberts (1986), Moorthy (1988), Bagwelland Riordan (1991), and Moorthy and Srinivasan(1995).4

4This implicitly assumes consumer risk neutrality and has beenmade for analytical simplicity. If consumers were risk averse, the H-type entrant would have a higher incentive to signal while the L-type entrant would have a higher mimicking incentive. Thus, if theincumbent were to signal-jam, he would have to distort his pricesup even further. This would mean even more “muted” initial reac-tion, thereby accentuating the phenomena of delayed defensive re-action. We thank an anonymous reviewer for alerting us to this issue.



Table 1 Demand Facing the Incumbent and the Entrant

Demand Functions

qI . qE

Incumbent’s Demandp 1 pI ED (p , P ) 4 1 1I I E q 1 qI E

(T1.1)

Entrant’s Demandp 1 p p q p 1 p qI E E E I E ID (p , p ) 4 1 4E I E q 1 q q q (q 1 q )I E E E I E

(T1.2)

qE . qI

Incumbent’s Demandp 1 p p q p 1 q pE I I I E E ID (p , p ) 4 1 4I I E q 1 q q q (q 1 q )E I I I E I

(T1.3)

Entrant’s Demandp 1 pE ID (p , p ) 4 1 1E I E q 1 qE I

(T1.4)

2.2. Demand Functions for the Incumbent and theEntrant

Consider the demand for a product of quality q at pricep when only one brand is available (as is the case inthe pre-entry period when the incumbent, firm I, is themonopolist). The set of consumers who will buy theproduct is of the form [h*, 1] where h* 4 min {h: 0 #

h # 1, hq 1 p $ 0}. Hence, in the pre-entry period, thedemand facing the incumbent, when he is the monop-olist, is given by (p) 4 1 1 (p/qI), where the su-PEDI

perscript PE refers to the pre-entry market structure.However, when more than one quality is offered in

the market (as is the case following the entry of theentrant firm, firm E), an individual consumer has todecide not only whether to buy at all but also selectbetween the incumbent’s and the entrant’s products.In this case, we need to ascertain that consumer pur-chase decision satisfies two key constraints. The firstcondition is the Individual Rationality (IR) or partici-pation constraint, which requires that for a consumerto purchase the product, he/she must derive a non-negative surplus. The second condition is the IncentiveCompatibility (IC) or self-selection constraint, whichrequires that if a consumer selects a product amongvarious alternatives, it must be that he/she derives thehighest surplus from the selected alternative.

Consider first the case of an incumbent offeringquality qI (at price pI) and the entrant offering qualityqE (at price pE) when the incumbent’s product is of su-perior quality, i.e., qI . qE. It is obvious that for theentrant to have a nonzero market share, it is necessarythat the entrant’s price be less than the incumbent’s,i.e., pE , pI. However, the condition pE , pI alone isnot sufficient to ensure that the entrant will enjoy anonzero market share. When qI/pI $ qE/pE (i.e., “qual-ity per dollar” is higher for the incumbent’s product),all consumers h [ [0,1] prefer the incumbent’s productto the entrant’s product, provided they purchase anyproduct because

hqI(hq 1 p ) 1 (hq 1 p ) 4 p 1 1I I E E I 1 2pI

hq hqE E1 p 1 1 $ (p 1 p ) 1 1E I E1 2 1 2p pE E

q qI E$ 0 •• $ .1 2• p pI E

In this case, the demand for the incumbent’s productis DI(pI, pE) 4 1 1 (pI/qI) and the demand for the en-trant’s low-quality product is zero. Now, consider thecase when the entrant’s product is not dominated, i.e.,qE , qI, pE , pI, and qI/pI , qE/pE. In this case, the setof consumers who purchase the incumbent’s productis of the form [h***, 1], where

h*** 4 min {h: 0 # h # 1, hq 1 p $ 0,I I

hq 1 p $ hq 1 p },I I E E

while the set of consumers purchasing entrant’s prod-uct is of the form [h**, h***] with 0 , h** , h*** , 1and

h** 4 min {h: 0 # h # 1, hq 1 p $ 0},E E

and the set of potential consumers who do not buy theproduct at all is [0, h**]. Note that the IC constraint istrivially satisfied for the buyers of the entrant’s prod-uct. Thus, the demand functions facing the incumbentand the entrant with qualities qE , qI are given byEquations (T1.1) and (T1.2) in Table 1.

Now consider the case when the entrant’s productis of superior quality. In this case, for the incumbentto have a nonzero market share, it must be that pE .pI and qI/pI . qE/pE.5 Under these conditions, the de-mand functions facing the incumbent and the entrantare given by Equations (T1.3) and (T1.4) in Table 1.

5In our analysis, we make the routine assumption that the cost ofquality function is convex. We further assume that this relationshipis sufficiently convex such that the quality per unit price is higherfor the lower quality product.



In the above discussion, we have assumed that thequality of the entrant’s product is known to the con-sumers. However, immediately following the entry offirm E, consumers may be uncertain about the en-trant’s quality. Let q [ [0,1] be the prior probabilitythat the true quality of the entrant is high and let 1 1

q [ [0,1] be the probability that the entrant’s quality islow.6 In this situation, the demand facing the entrant(and the incumbent) would depend on the consumers’beliefs about the entrant’s quality q̃E rather than theentrant’s true quality qE and hence the demand func-tions for the incumbent and the entrant can be obtainedby substituting q̃E for qE in the above demandfunctions.

Observe that the demand function facing the en-trant, DE(.,.) (both when qE , qI, Equation (T1.2), andwhen qE . qI, Equation (T1.4)), is increasing in the per-ceived quality qE of the entrant’s product. This sug-gests that when the entrant’s quality is uncertain, ahigh-quality entrant stands to gain (through demandenhancement) by favorably changing the quality per-ception of her product. This provides the necessary in-centive for quality signaling by a high-quality entrant,provided she can credibly do so and signaling is notprohibitively expensive. Furthermore, the demandfunction facing the incumbent, DI(.,.) (both when qE ,qI, Equation (T1.1), and when qE . qI, Equation (T1.3)),is decreasing in the perceived quality qE of the entrant’sproduct so that any favorable change in the entrant’sperceived quality hurts the incumbent. Thus, if the in-cumbent, through his strategic choice of marketing-mix variables, can increase the cost of quality signalingby a high-quality entrant, he would optimally do so.This provides the intuition behind the “signal-jamming” effort by an incumbent who knows the“true” high quality of the entrant in the face of (im-plicit) quality-signaling threat from a high-quality en-trant. We summarize the above observation on the im-plications of entrant’s perceived product quality on the

6Consumers’ priors may arise from their experience from relatedproducts: For example, consumers can base their expectations on thepossible quality levels of computer monitors from televisions, of faxmachines from photocopying machines, etc.

incumbent’s and entrant’s demand in the followinglemma:7

Lemma 1. The demand for the entrant’s product is in-creasing in the (perceived) quality of the entrant’s product,qE, while the demand for the incumbent’s product is decreas-ing in qE, i.e., ]DE/]qE . 0, and ]DI/]qE , 0.

3. AnalysisIn § 3.1, we first describe the optimal pricing strategiesof the incumbent and the entrant firm when consumersare aware of the quality of the entrant’s product. Theanalysis serves to characterize the optimal “defensivereaction” of the incumbent firm when signal jammingis not a key strategic consideration. In § 3.2, we relaxthe assumption that consumers know the entrant’squality and analyze the implications for the optimalpricing strategies of the incumbent and the entrant us-ing a two-period model. We assume that consumersare uncertain about the entrant’s product at the begin-ning of the first period (i.e., immediately following theentry of the new firm) while the quality of the entrantgets revealed over time (i.e., at the beginning of thesecond period). Our analysis shows that, under con-ditions of incomplete information about the entrant’squality, it may be optimal for the incumbent to delayhis reaction. In this case, the adjustment in the incum-bent’s pricing strategy from the pre-entry to the post-entry levels does not occur immediately but ratherover an extended time frame. This temporal pattern ofincumbent’s price underlies the notion of delayed(price) reaction.

3.1. Equilibrium Analysis When the Entrant’sQuality Is Known

In the pre-entry period, the incumbent firm is a mo-nopolist and as such charges a price that maximizeshis profit. Since the focus of our analysis is to studythe defensive reaction of the incumbent following theentry of a new firm, we assume that limit pricing(Milgrom and Roberts 1982; Srinivasan 1991) is not an

7Proof of all the lemmas and the propositions are given in the ap-pendix.



Table 2 Competitive Pricing Strategies of the Entrant and theIncumbent Under Complete Information (Programs P1 andP2)

ParametricCondition Competitive Pricing Strategies

qI . qE Incumbent’s Pricing Problemp 1 pI EP1 : p* [ argmax P (p , p ) [ (p 1 c ) 1 1I I I E I I 3 4q 1 qp I EI

(T2.1)

Entrant’s Pricing Problemq p 1 q pE I I EP18 : p* [ argmax P (p , p ) [ (p 1 c )E E I E E E 3 4q (q 1 q )p E I EE

(T2.2)

qE . qI Incumbent’s Pricing Problemq p 1 q pI E E IP2 : p* [ argmax P (p , p ) [ (p 1 c )I I I E I I 3 4q (q 1 q )p I E II

(T2.3)

Entrant’s Pricing ProblemP 1 pE IP28 : p* [ argmax P (p , p ) [ (p 1 c ) 1 1E E I E E E 3 4q 1 qp E IE

(T2.4)

issue and hence firm I cannot deter entry.8 The follow-ing lemma characterizes the optimal pre-entry price ofthe incumbent firm:

Lemma 2. The optimal pricing strategy of firm I (in-cumbent) in the pre-entry period when he is a monopolist isgiven by 4 (qI ` cI)/2, where the superscript PE refersPEpI

to the pre-entry market structure and cI is his marginal cost.

In the post-entry period, however, is no longer thePEpI

optimal pricing strategy for firm I due to the funda-mental change in the market structure. The equilib-rium prices of the incumbent and the entrant firms inthe post-entry period will critically depend on the rela-tive qualities of the entrant’s and the incumbent’sproduct. Let qI and qE be the qualities of the incum-bent’s and the entrant’s products and let cI and cE betheir respective marginal costs. Then, the followingtwo situations may arise: (a) entrant’s product is of in-ferior quality, i.e., qI . qE, and (b) entrant’s product isof superior quality, i.e., qI , qE.

First, we consider the case when the incumbent’sproduct is of superior quality. The pricing problemfaced by the incumbent, for any given price of the en-trant, pE, can be formulated as Program P1 given inTable 2 (Equation (T2.1)).

Thus, the reaction function of the incumbent whilecompeting against an entrant with an inferior productis given by

R (p ) [ 2p 1 q ` q 1 p 1 c 4 0. (1)I I I I E E I

Note that the incumbent’s reaction function RI(•) is in-creasing in the entrant’s price, pE, i.e.,

]R (•) ]pI I[ . 0. (2)]p ]pE E

Since both the entrant and the incumbent select theirduopoly prices simultaneously, the entrant faces asimilar situation. The pricing problem faced by the en-trant, for any given price set by the incumbent, pI, can

8This implicitly assumes that the cost structure of the incumbent isknown to firm E before making the entry decision. This is reasonablebecause from the pre-entry pricing strategy of the incumbent firm,the entrant can infer the marginal cost of the incumbent. In the ab-sence of asymmetric information on the marginal cost of the incum-bent, limit pricing in the sense of Milgrom and Roberts (1982) andSrinivasan (1991) is not an equilibrium outcome.

be similarly formulated as Program P18 given in Table2 (Equation (T2.2)).

Thus, the reaction function of the entrant while com-peting against an incumbent with a superior productis given by

R (p ) [ 2q p 1 q p 1 c q 4 0. (3)E E I E E I E I

It is easy to show that the entrant’s reaction functionRE(•) is increasing in the incumbent’s price as well asincreasing in the entrant’s quality and marginal cost,i.e.,

]R (•) ]p ]R (•) ]pE E E E[ . 0; [ . 0,]p ]p ]q ]qI I E E

and

]R (•) ]pE E[ . 0. (4)]c ]cE E

Equations (2) and (4) reflect the fact that underBertrand competition, the reaction functions are up-ward sloping, implying that pricing strategies of theincumbent and the entrant are strategic complements(Fudenberg and Tirole 1984; Bulow, Geanakoplos, andKlemperer 1985).9 The Nash-equilibrium prices of the

9We thank an anonymous reviewer for this observation.



Table 3 Equilibrium Prices of the Entrant and the Incumbent UnderComplete Information

ParametricCondition Equilibrium’s Pricing Strategies

qI . qE Incumbent’s Price2q (q 1 q ) ` q (2c ` c )I I E I I Ep* 4I 4q 1 qI E

(T3.1)

Entrant’s Price

.q (q 1 q ) ` c q ` 2c qE I E I E E Ip* 4E 4q 1 qI E

(T3.2)

qE . qI Incumbent’s Price2q c ` q (q 1 q ` c )E I I E I Ep* 4I 4q 1 qE I

(T3.3)

Entrant’s Price2q (q 1 q ) ` q (2c ` c )E E I E E Ip* 4E 4q 1 qE I

(T3.4)

incumbent and entrant are a pair of prices that simul-taneously satisfy the incumbent’s and the entrant’s re-action functions. The following proposition character-izes the optimal pricing strategies of the incumbentand the entrant when the incumbent’s product issuperior:

Proposition 1. The equilibrium post-entry prices forthe incumbent and the entrant when the consumers knowthe entrant’s true quality and the incumbent’s product is ofsuperior quality are as given by Equations (T3.1) and (T3.2),respectively, in Table 3.

Now, consider the case when the entrant’s product isof superior quality. In this case, the optimal pricingstrategies faced by the incumbent and the entrant canbe modeled as Programs P2 and P28 given in Table 2(Equations (T2.3) and (T2.4), respectively).

As in the previous case, it can be shown that whenqI , qE the reaction functions for the incumbent andthe entrant are given by

R (p ) [ 2q p 1 q p 1 c q 4 0, (5)I E E I I E I E

and

R (p ) [ 2p 1 q ` q 1 p 1 c 4 0, (6)E I E E I I E

respectively. It can be further shown that these reactionfunctions are upward sloping in the competitive price.The following proposition characterizes the optimal

pricing strategies of the incumbent and the entrantwhen the entrant’s product is superior:

Proposition 2. The equilibrium post-entry prices forthe incumbent and the entrant when the consumers knowthe entrant’s true quality and the entrant’s product is ofsuperior quality are as given by Equations (T3.3) and (T3.4),respectively, in Table 3.

As the following proposition demonstrates, the incum-bent’s optimal price in the post-entry period is alwayslower than in the pre-entry period regardless ofwhether he faces an entrant with a superior product oran entrant with an inferior product:

Proposition 3. The optimal defensive strategy for theincumbent following the entry of a new firm, when consum-ers know the quality of the entrant’s product, is to imme-diately reduce his price to the optimal duopoly price. Thepost-entry price of the incumbent is lower than his pre-entryprice, i.e., . .PEp p*I I

Proposition 3 implies that when consumers know theentrant’s quality with certainty, the incumbent’s reac-tion will be immediate. Once the incumbent has ad-justed his pricing strategy from the pre-entry monop-oly level to the post-entry duopoly level, he wouldhave no incentive to change his pricing strategy. Thus,when the entrant’s quality is known, a delayed priceresponse from the incumbent is not optimal.

3.2. Equilibrium Analysis When the Entrant’sQuality Is Uncertain

We now consider the more general case of post-entryprice competition between the incumbent and the en-trant when consumers are uncertain about the en-trant’s quality. This is a reasonable assumption, espe-cially when the firm sponsoring the new product is nota reputed firm. Consumers know the quality of the in-cumbent’s product, qI, through their prior experiencewith that product. We, however, assume that the in-cumbent is aware of the true quality of the entrant’sproduct. The rationale for our assumption about theasymmetry across consumers and the incumbent re-garding the entrant’s quality is as follows: Recall thatthe attribute characterizing the product in quality-sig-naling literature (Milgrom and Roberts 1986; Bagwelland Riordan 1991; Moorthy and Srinivasan 1995) is



conceptualized as an experience attribute, i.e., that di-mension of a product’s quality that cannot be ascer-tained prior to purchase/consumption. However, theconsumer learns the true level of the attribute throughconsumption experience. Our analysis rests on the no-tion that the incumbent firm can ascertain the truequality of the entrant’s product easily through me-chanical testing or reverse engineering. Doing so, how-ever, is prohibitively costly for an individualconsumer.

To capture the consumer uncertainty regarding theentrant’s quality, we assume that qE [ { , }, whereH Lq qE E

denotes the quality of the entrant’s product if theHqE

entrant is a high-quality firm and denotes the qual-LqE

ity of the entrant’s product if she is a low-qualityfirm.10 We further assume that . . 0. Let q [H Lq qE E

[0,1] be the prior probability that the true quality of theentrant is high and 1 1 q [ [0,1] be the probabilitythat the entrant’s quality is low. We assume that thequality of the entrant gets revealed at the beginning ofPeriod 2 provided some consumers buy the entrant’sproduct in Period 1.11 Consistent with prior signalingliterature (Milgrom and Roberts 1986; Moorthy andSrinivasan 1995), we assume that . . 0,12 whereH Lc cE E

and are the marginal costs of the high-quality andH Lc cE E

10In reality, consumer uncertainty regarding the entrant’s qualitywill be manifested through qE belonging to a range [qE, q̄E] with 0 ,

qE , q̄E. Consistent with the signaling literature, for analytical sim-plicity, we capture uncertainty by hypothesizing that qE [ { , }.H Lq qE E

11Our assumption that the entrant’s quality gets fully revealed at thebeginning of Period 2, while consistent with extant quality-signalingliterature (Milgrom and Roberts 1986; Moorthy and Srinivasan 1995),is clearly an abstraction of reality. Note that in these two-periodstylized models, time period needs to be interpreted in an informa-tional sense rather than a temporal sense. Further, if in our model,entrant’s quality were to be gradually revealed over time throughword of mouth in the spirit of Bagwell and Riordan (1991), we con-jecture that this would imply that the incumbent’s price, instead ofdropping instantaneously in Period 2 in the current formulation,would converge more gradually to the full-information duopolylevel. This would observationally imply further “delay” in the in-cumbent’s defensive response. We thank an anonymous reviewerfor alerting us to this issue.12The basic idea behind this assumption of perfect correlation be-tween quality and cost is that higher quality entails higher cost ofproduction. This implicitly assumes that lower quality of the entrantis not attributable to technological inefficiencies. We thank anony-mous reviewers for suggesting clarification on this issue.

low-quality entrants, respectively. For notational con-venience, we shall refer to the high-quality entrant asthe H-type entrant and the low-quality entrant as theL-type entrant.

Our analysis under asymmetric information aboutthe entrant’s quality underscores the following issues:As in the monopoly case (Wolinsky 1983; Bagwell andRiordan 1991; Bagwell 1991), the H-type entrant cansignal her high quality by distorting her initial post-entry price upwards in the duopoly case as well. How-ever, unlike in the previous cases, the incumbent whoknows the “true” quality of the entrant can manipulatethe signaling cost of the H-type entrant by distortinghis initial post-entry prices upwards. Thus, under cer-tain parametric conditions, the incumbent can increasethe H-type entrant’s signaling cost. In fact, when theH-type entrant’s signaling cost is sufficiently raised,the entrant’s attempt to signal quality may no longerbe optimal. We call such equilibrium the signal-jam-ming (SJ) equilibrium.13 Because of signal jamming, theinitial post-entry price of the incumbent is higher thanthe (long-term) equilibrium duopoly levels. After theentrant’s quality gets revealed through word of mouth,the incumbent reduces his prices to the duopoly levels.We interpret this temporal pattern of incumbent’sprice wherein the incumbent “reacts” to competitiongradually over time as ‘delayed’ defensive response.

We obtain these results by employing the sequentialequilibrium concept (Kreps and Wilson 1982). Essen-tially, the concept requires that (a) each type of entrantfirm selects her optimal pricing strategies, given opti-mal action on the part of the incumbent firm and theconsumers; (b) the incumbent selects his optimal pric-ing strategy, given optimal type-contingent strategiesof the entrant firm and optimal strategies of the con-sumers; (c) individual consumers make optimal buy/no buy decisions given the optimal pricing strategiesof the H-type and L-type entrant firms and the incum-bent firm and given their beliefs about the entrant’s

13Note that this definition of signal-jamming is somewhat differentfrom that of Fudenberg and Tirole (1986). Unlike in their case, thesignal-jamming action (incumbent’s first-period pricing) is observ-able (though, in SJ equilibrium, it is not informative since his pricesare the same whether it is the H-type or the L-type entrant). It issimilar to Fudenberg and Tirole (1986) in the sense that signal jam-ming interferes with the inference problem faced by the uninformedplayer (entrant in their model, consumers in this model).



type; and (d) wherever possible, consumers updatetheir beliefs about the entrant’s type using Bayes’ rule.In the following analysis, we restrict our attention toequilibria arising from pure strategies. The focus of ouranalysis is on the so-called separating and pooling se-quential equilibria. In a separating equilibrium, thefirst-period pricing strategies of the two types of theentrant differ and, therefore, consumers can correctlyinfer the entrant’s quality. On the other hand, in a pool-ing equilibrium, the first-period pricing strategies ofthe H-type and the L-type entrants are the same and,therefore, consumer posterior belief is the same as theprior belief. Note that the Bayesian updating allowsarbitrary beliefs for out-of-equilibrium paths, raisingthe possibility of a multiplicity of equilibria (Tirole1988). We employ the refinement of “elimination ofdominated strategies” (Moulin 1979) and the “intuitivecriterion” (Cho and Kreps 1987) to eliminate sequentialequilibria supported by implausible out-of-equilibrium beliefs.

3.2.1. Quality Uncertainty and Strategic Consid-erations of the Entrant and the Incumbent. Unlikethe case when the entrant’s quality is known with cer-tainty, the strategic considerations facing the entrantand the incumbent are more involved. We discuss nextthe incentive for the high-quality entrant to engage inquality signaling and the conditions under which suchsignaling is possible (i.e., in technical terms, conditionsfor satisfaction of Spence-Mirrlees “single-crossing”property). We then discuss the incentive for the incum-bent to engage in signal jamming and conditions underwhich this is possible.

3.2.1.1. Entrant’s Incentive and Ability to Signal Qualityin Duopoly. When consumers a priori are uncertainabout the quality of the entrant’s product, they basethe purchase decision on qI and the expected qualityof the entrant’s product, q̃E [ .14 SinceH Lqq ` (1 1 q)qE E

. q̃E, a high-quality entrant stands to gain by re-HqE

vealing her “true” higher quality. In the followingproposition, we summarize this result, which provides

14This simplification in the derivation of realized demand for theincumbent’s and the entrant’s products is due to the assumption ofconsumers’ risk-neutrality. If consumers were risk averse, demanduncertainty will reduce the entrant’s demand even further, therebyincreasing the gains accruing to a high-quality entrant from qualitysignaling. We thank an anonymous reviewer for this insight.

the requisite incentive for the high-quality entrant toengage in quality signaling.

Proposition 4. The optimal profit of the high-qualityentrant is increasing in her perceived quality given the priceof the incumbent, i.e., /]q̃E . 0.H]P *E

However, since both the high- and low-quality en-trants stand to gain from favorable consumer beliefs,a mere assertion of superior quality will be discountedby rational consumers and hence cannot serve as acredible signal of high quality.15 The H-type entrantcan convey her superior quality by increasing, for anygiven price pI of the incumbent, her first-period priceabove her optimal price under complete information.The basic intuition is as follows: Recall that the mar-ginal cost of the H-type entrant is higher than that ofthe L-type entrant, i.e., . As such, under con-H Lc . cE E

sumer uncertainty about the entrant’s quality so thatthe price charged by the H- and the L-type is the same(being consistent with q̃E), for any price pE selected bythe entrant, the per unit contribution margin is higherfor the L-type entrant than for the H-type entrant.Therefore, the opportunity cost of a loss in sales ishigher for the L-type entrant. Thus, to deter mimickingfrom a possible L-type, the H-type entrant distorts thefirst-period prices to a higher level so as to limit thesales in the first period.16 Our analysis suggests thatthe intuition behind higher price as a signal of higherquality is valid even under duopolistic market condi-tions. We formally demonstrate this result in the fol-lowing proposition:

Proposition 5. For any given price of the incumbent,pI, the marginal losses resulting from any marginal upwardprice distortion are greater for the L-type entrant than forthe H-type entrant. Therefore, for prices above the optimalprice of the H-type entrant under complete information, the

15Note that in our stylized product market, there is only one entrant:either a H-type entrant or a L-type entrant. However, since consum-ers a priori do not know the entrant’s true quality, the H-type entranthas to select an appropriate pricing strategy to credibly convince theuncertain consumers that she indeed is a H-type entrant.16Intuitively, the L-type entrant would want to adopt the strategy ofa fly-by-night operator of selling as many units as possible beforeher true low quality gets revealed. Thus, to achieve a separation, theH-type entrant adopts the costly strategy of selling less than hercomplete information quantity by charging a higher price.



L-type entrant incurs greater losses than the H-type entrant,i.e.,

L L H H]P (q̃ , p , c ) ]P (q̃ , p , c )E E I E E E I E$ 1@]p ]pE E

H*for ∀ p $ p , (7)E E

where is the H-type entrant’s optimal price when theH*pE

entrant’s quality is known with certainty.

The implication of Proposition 5 is that by distortingher price, pE, “sufficiently” above the complete infor-mation price level, , the high-quality entrant canHp *E

deter mimicking from a “ghost” low-quality entrant.Thus, in the resulting separating equilibrium, the twotypes of entrants follow different pricing strategies.Therefore, by observing a “high” price, rational con-sumers correctly infer that the entrant’s quality is high.

3.2.1.2. Incumbent’s Incentive and Ability to Signal Jam.The key difference in the entrant’s quality signalingstrategy between monopoly and duopoly is note-worthy. Under duopoly, the high-quality entrant’smarginal ability to separate from the “ghost” low-quality entrant depends on the pricing strategy of theincumbent. Essentially, the incumbent can “suffi-ciently” increase the high-quality entrant’s cost ofquality signaling such that quality signaling is too ex-pensive to undertake. Recall, that the incumbent firmknows the entrant’s true quality. Further, the incum-bent recognizes the signaling incentive on the part ofthe H-type entrant. It is important to note that whenconsumers recognize a high-quality entrant correctly,the incumbent’s profit is lower. Therefore, the incum-bent has an incentive to prevent the entrant from cred-ibly signaling her quality.

Proposition 6. The profit of the incumbent is decreas-ing in the perceived quality of the entrant given the price ofthe entrant, i.e., (•)/]q̃E , 0.]P *I

The signaling cost borne by the H-type entrant de-pends on the H-type’s marginal ability to separate,which is defined as the ratio of /]pE to /]pE.L H]P ]PE E

If, through his pricing strategy, the incumbent can re-duce the H-type entrant’s marginal ability to separate,the incumbent can increase the signaling cost of the H-type entrant, thereby making quality signaling more

difficult. (As we note in the following proposition, theH-type entrant’s marginal ability to separate is de-creasing in the incumbent’s prices.)

Proposition 7. The high-quality entrant’s marginalability to separate decreases as the incumbent’s priceincreases.

The intuition behind this result is as follows: The ratioof the slopes of the L-type entrant to the H-type entrantdecreases as the H-type entrant’s price increases. Asnoted earlier, since pricing strategies of the incumbentand the entrant are strategic complements (Fudenbergand Tirole 1984; Bulow, Geanakoplos, and Klemperer1985), the H-type entrant’s prices are increasing in theincumbent’s prices. By distorting his prices upward,the incumbent raises the H-type entrant’s price(through the competitive effect), thereby reducing theH-type entrant’s marginal ability to separate from theL-type entrant.

Proposition 8. The low-quality entrant’s incentive tomimic the high-quality entrant increases as the incumbent’sprice increases.

Note that Proposition 7 suggests that the H-type en-trant’s ability to separate is reduced by upward pricedistortion by the incumbent. Moreover, Proposition 8states that the L-type entrant enjoys greater incentiveto pool with the H-type entrant. When taken together,these results clearly underscore the incentive for theincumbent to engage in signal jamming. The incum-bent does it by selecting a price sufficiently high suchthat separation for the entrant is so costly that she pre-fers to pool. Clearly, the existence of such a signal-jamming equilibrium will depend upon certain para-metric conditions. As will become evident from thenext section, the signal-jamming equilibrium prices arecomplex expressions and, therefore, we are unable toexpress the condition in a tractable way. We rely onnumerical simulations to verify existence of signal-jamming equilibrium over a range of parametervalues.

Note that the incumbent facing a true L-type entrantmay want to signal the entrant’s type to consumers.However, the incumbent cannot credibly do so bychoosing a price higher than the signal jamming price.The reason is that the marginal losses to the incumbent



Table 4 Quality-Signaling Pricing Strategy of the High-QualityEntrant Under Incomplete Information (Program P3)

P3:H Hq p 1 q pE I I EQSH H H H Hp [ argmax P (p , p ) [ (p 1 c )HE E I E E E 3 4H Hq (q 1 q )p E I EE

(T4.1)

subject toH Hq p 1 q pE I I EL,H H LP (p ) [ (p 1 c ) 2E I E E 3 4H Hq (q 1 q )E I E

.L L,*q p 1 q p (p )E I I E IL,* L L,L# [p (p ) 1 c ] 2 [ P (p )E I E E I3 4L Lq (q 1 q )E I E

Table 5 Signal-Jamming Pricing Strategy of the Incumbent UnderIncomplete Information (Program P3*)

P3*:p 1 pI ESJp [ argmax P (p , p ) [ (p 1 c ) 1 1I I I E I I 3 4q 1 q̃P I EI

(T5.1)

subject toQSH Hq p 1 q p (p )E I I E IQSH,H H HP (p ) [ (p (p ) 1 c )E I E I E 3 4H Hq (q 1 q )E I E

H,qq̃ p 1 q p (p )E I I E IH,q H H,q# (p (p ) 1 c ) [ P (p ).E I E E I3 4q̃ (q 1 q̃ )E I E

(T5.2)

from such an upward price distortion are the same forboth types of entrants.

3.2.2. Quality Uncertainty, Signal Jamming, andDelayed Defensive Reaction. Essentially, the in-cumbent signal jams the quality-signaling efforts of theH-type entrant by distorting his first-period priceabove his complete-information duopoly price. In thesecond period, however, the quality of the entrant getsrevealed provided the entrant enjoys nonzero sales inthe first period.17 Therefore, the incumbent’s pricesconverge to the equilibrium duopoly prices. We inter-pret this temporal pattern of the incumbent’s price re-sponse occurring in the second period (instead of im-mediately following entry) as the empirically observedphenomenon of delayed reaction by the incumbent inthe face of competitive entry.

3.2.3. Characterization of the Signal-JammingEquilibrium. In this section, we characterize the op-timal pricing strategies for the incumbent and the H-and L-type entrants under the condition Hq . q .I E

. Note that under this parametric condition, the in-LqE

cumbent’s quality is superior to the entrant’s perceivedquality, i.e., qI . q̃E. The logic for the case .H Lq . qE E

qI is similar and, for brevity, we omit the analyticaldetails.

Before we offer details of our analysis, we describethe logic behind our approach. First, in Program P3(Table 4), we obtain the reaction function of the H-typeentrant to any given price of the incumbent when theH-type entrant attempts to achieve least-cost separa-tion. Subsequently, in Program P38 (Table 5), we derivethe incumbent’s signal-jamming reaction function forany given price of the entrant. Moreover, the reactionfunction satisfies the constraint that the H-type entrantweakly prefers the pooling outcome to engaging in

17In this paper, we do not consider the case when the incumbent,through manipulating his first-period price, can completely blockout the entrant, i.e., the entrant has zero sales in the first period (asalso in subsequent periods since the entrant’s true high quality nevergets revealed). If indeed zero sales for the entrant (i.e., entrant’s exitfrom the market) were to occur in equilibrium, then entry of firm Ein the first period cannot be an optimal strategy. Furthermore, suchpredatory pricing by the incumbent is illegal under section 2 of theSherman Act. Alternatively, we can assume that in Period 2, theentrant’s quality is always known with certainty.

quality signaling. The pair of prices obtained by si-multaneously satisfying the two reaction functionsconstitute the signal-jamming equilibrium.

In Figure 1, we graphically represent the signal-jamming equilibrium. The curves in this figure repre-sent the reaction functions of the incumbent and en-trant, identified by appropriate subscripts, for thevarious informational scenarios. (pI)( (pI)) rep-H,* L,*R RE E

resents the high-quality (low-quality) entrant’s reac-tion function under complete information (obtained bysubstituting ( ) and ( ) for qE and cE, respec-H L H Lq q c cE E E E

tively, in Equation (3)). (pI) represents the H-typeH,qRE

entrant’s reaction function consistent with prior beliefs(obtained by substituting q̃E and for qE and cE, re-HcE

spectively, in Equation (3)). (pI) represents the re-QSRE

action function for the high-type entrant correspond-ing to least-cost separation (see Lemma 3; Equation(8)). (pE) represents the incumbent’s reaction func-R*Ition when it refrains from signal jamming (cf. Equation(1)). Finally, (pE) is the incumbent’s reaction func-SJRI

tion under signal jamming (see Lemma 4; Equation(11)).



Figure 1 Schematic Representation of the Complete Information and Asymmetric Information Equilibria

3.2.3.1. Optimal Pricing Strategy of the High-QualityEntrant Under Quality Signaling. We first consider thereaction function of the H-type entrant when she en-gages in signaling her high quality through upwarddistortion of the first-period price. Let pI be any givenprice of the incumbent. Then, the pricing problemfaced by the H-type entrant, given pI, when she at-tempts to credibly signal her quality can be modeledas Program P3 in Table 4.

The logic behind the program formulation P3 is asfollows: Constraint (T4.2) denotes the mimicking con-straint for the L-type entrant. The left-hand side ofEquation (T4.2) represents the L-type’s profit, given pI,when she mimics the H-type’s pricing strategy and,under the most favorable consumer beliefs, she is mis-taken to be the H-type entrant (see Moorthy andSrinivasan (1995) for additional discussion on the issueof formulating the L-type’s mimicking constraint). Wedenote this profit by (pI) where the first super-L,HP E

script denotes the L-type entrant’s true type, while thesecond superscript denotes consumer beliefs about theL-type under mimicking. The rationale behind takingthe price of the incumbent, pI, as given is the Nashassumption of zero conjectural variation (Iwata 1974;Bresnahan 1987). The right-hand side of Equation(T4.2) represents the L-type’s profit, for any given pI,when she selects her complete-information price andconsumers correctly infer her low quality, i.e., . WeLqE

denote this profit since both the entrant’s trueL,LP E

(first superscript) and the perceived (second super-script) quality type is the L type.

Lemma 3. The optimal pricing strategy of the H-type,given pI, when she attempts to signal her high quality (atthe least-cost signaling) is given by

H H Lp q (1 ` l ) ` q (c ` l c )QS I E 1 I E 1 EHp (p ) 4 , (8)E I 2q (1 ` l )I 1

where l1 [ (11, 0) is given by



l 4 11 `I

H L 2 H H H H H L 2 H L(q p 1 c q ) ` (q p ` c q )(c q 1 q p ) 1 2c c q ` 2p q q cE I E I E I E I E I E I E E I I I E E .H L 2 H H! (q p 1 c q ) 1 4kq q (q 1 q )E I E I E I I E

(9)

Note that lI, which essentially reflects the “tightness”of the IC constraint of the L-type entrant, denotes theextent of distortion in the H-type’s price required forcredible quality separation (for any given price of theincumbent, pI). Thus, lI 4 0 corresponds to the casewhen the mimicking constraint is non-binding so thatthe H-type entrant can achieve quality separation with-out any distortion. An immediate implication of Equa-tion (9) is that ]lI/]pI , 0, which implies that the sig-naling cost borne by the H-type entrant is increasingin the incumbent’s price (or, equivalently, the IC con-straint of the L-type entrant is “tighter”). Therefore, theincumbent can raise his price in order to make qualitysignaling more expensive for the high-quality entrant.Furthermore, it can be shown that the H-type entrant’sreaction function under quality signaling (as given byEquation (8)) is steeper than that under complete in-formation (as given by Equation (3)). Thus, for anygiven price of the incumbent, pI, the H-type entrantselects a higher price under quality signaling. This re-sult is consistent with the upward price distortion ob-tained in the literature under monopoly conditions(e.g., Wolinsky 1983; Bagwell and Riordan 1991;Bagwell 1991; Judd and Riordan 1994). We summarizethese insights in the following lemma:

Lemma 4. The higher the incumbent’s price, pI, thegreater in the extent of distortion in the H-type entrant’sprice needed for credible quality signaling, i.e., ]lI/]pI , 0.Furthermore, the H-type entrant’s reaction function issteeper under quality signaling than under completeinformation

QSH H,*]p ]pE E1 [

]p ]pI I

H H L 2 H Lq q (c 1 c ) [p q 1 q c ]I E E E I E I E2 22 H H L H H L 3/22(1 ` l ){p q 1 2p q q c ` q [4kq (q 1 q ) ` q c ]}1 I E I E I E I E E I I E

. 0. (10)

Thus, for any given incumbent’s price, pI, the H-type en-trant selects a higher price under quality signaling than un-der complete information.

3.2.3.2. Optimal Pricing Strategy of the Incumbent Un-der Signal Jamming. When the incumbent engages insignal jamming, for any given entrant’s price pE, thestrategic consideration facing the incumbent is notonly to maximize his profit but also to select a price“high enough” to deter quality signaling by the H-typeentrant. The incumbent’s pricing problem when he at-tempts to jam the entrant’s quality signaling can bemodeled as Program P38 given in Table 5.

In Equation (T5.2), (pI) refers to the H-type en-H,qpE

trant’s reaction function when consumers believe herquality to be q̃E and is obtained from Equation (3) (bysubstituting q̃E for qE and for cE). (pI) is the H-QSH Hc pE E

type entrant’s quality-signaling reaction and is givenby Equation (8). Constraint (T5.2) is the IC constraintfor the H-type entrant, which requires that the H-typeentrant prefers to “pool” with the L-type entrant byfollowing the pricing strategy (pI) rather than toH,qpE

reveal her high quality by engaging in quality-signaling pricing strategy (pI). We denote the profit

QSHpE

of the H-type entrant under pooling by (pI); the H-H,qPE

type’s profit when her high quality gets revealed isdenoted by (pI).H,HPE

Note that in the above program we do not need toimpose an additional constraint to ensure that the in-cumbent prefers signal jamming even when he knowsthat the entrant is the L type. The reasoning is as fol-lows: Any low-quality entrant not only realizes thehigh-quality entrant’s incentive to separate but also re-alizes the incumbent’s incentive to signal jam such aseparation. Suppose the incumbent did not engage insignal jamming, realizing the entrant’s quality to below. In that case, the low-quality entrant will mimicthe high-quality entrant’s optimal price, avoiding sep-aration, and force the incumbent to the signal-jammingprice to create weak defection to the first best. In otherwords, signal jamming by the incumbent makes sep-aration by the high-type costlier but makes mimickingby the L-type more attractive.18

18An alternative way of gleaning the intuition as to why the incum-bent will not defect from the signal-jamming equilibrium even whenhe faces a L-type entrant is stated in the spirit of the forward induc-tion in Cho and Kreps (1987). The L-type entrant makes the followingstatement to the incumbent: “I know that you will try to prevent theH-type entrant from signaling quality by choosing signal-jammingprices. Therefore, the only way the H-type entrant can signal quality



The following lemma characterizes the incumbent’sreaction function under signal jamming:

Lemma 5. The optimal pricing strategy of the incum-bent, for any given price of the entrant, when the incumbentattempts to jam quality signaling is given by

H2p 1 c ` q̃ 1 c 1 qI E E I I

H Hq (q 1 q̃ ) cE I E EH1 l ` p ` 4 0. (11)2 E3 H 42q (q 1 q ) 2I I E

The following proposition characterizes the signal-jamming equilibrium:

Proposition 9. In the signal-jamming equilibrium,the optimal prices of the incumbent and the entrant are givenby the simultaneous solution to Equations (8) and (11). Insuch a pooling equilibrium, both the H- and the L-type en-trants select the same price and consumers’ posterior beliefscoincide with their prior beliefs. Furthermore, the incumbentselects the same price, irrespective of the entrant’s qualitytype. This perfect Bayesian equilibrium is supported by thefollowing out-of-equilibrium beliefs pI ? ⇒ q 4 1 andSJpI

pE ? ⇒ q 4 0, which satisfy the intuitive criterion.SJpE

Note that in the signal-jamming equilibrium, both theH-type and the L-type entrants follow the same pricingstrategies. In other words, the H-type entrant “pools”with the L-type entrant. Since both the H-type and theL-type entrants follow the same strategy, the pricingstrategy of the incumbent is also not contingent on thequality type of the competing entrant firm. Further,observe that both the entrant and the incumbent followthe same pricing strategies, regardless of whether theentrant is the H type or the L type. Hence, on observingthe incumbent’s and the entrant’s prices, the consum-ers cannot rationally infer the entrant’s “true” quality.Therefore, consumers’ posterior beliefs coincide withtheir priors.

3.3. Numerical ExampleWe illustrate the delayed reaction with a numerical ex-ample. Let the quality of the incumbent product, qI, be200, the quality of the H-type entrant ( ) be 175, andHqE

is by selecting a price higher than the signal-jamming price. I exploityour desire to signal jam by mimicking any price equal to or lowerthan the signal-jamming price of the H-type entrant.”

that of the L-type entrant ( ) be 100. Furthermore, con-LqE

sumers are pessimistic about the entrant’s quality withprior probability, q, of 0.05 that the entrant’s quality ishigh. Note that such beliefs provide the incentive forthe H-type entrant to engage in quality signaling. Themarginal cost of the incumbent, cI, is 30, while those ofthe H- ( ) and L-type ( ) entrants are 18 and 5, re-H Lc cE E

spectively. Under these parametric conditions, the pre-entry monopoly price of the incumbent ( ) is 115,PEpI

while under duopoly the incumbent’s price when en-trant’s quality is known with certainty in Period 2 ( )p*Iis 40.96. The incumbent’s price in Period 1 to jam theentrant’s quality signal ( ) is 112.05. We also note thatSJpI

the incumbent’s profit under signal jamming improvesby 55% over the case when the incumbent allows theentrant to signal quality. Thus, the sequence of the ob-served price of the incumbent is 115 (pre-entry), 112.05(signal jamming), and 40.96 (complete information). Inthis example, of the total decrease in the incumbent’sprice of 74.04, only 4% of the price decrease occursimmediately after entry while 96% of the decrease oc-curs after entrant’s quality becomes known.

We repeated the numerical simulation for a large setof values for the parameters of the model. We find thatin most cases, a signal-jamming equilibrium exists. Wefind that the incumbent’s price path, consistent withthe phenomenon of delayed response, is quite robust.

4. Experimental ValidationThe observational implication of the model is that theoptimal strategy of the incumbent may be a delayeddefensive response. As discussed earlier, most of theempirical studies in the literature find significant delayin defensive reactions (Robinson 1988; Bowman andGatignon 1995), which can be viewed as confirmingour model predictions. Even though the empiricalstudies are not inconsistent, they do not constitute a“test” of the theory in the strict sense of the term. Forinstance, in the existing data sets (e.g., PIMS) we donot know the extent of consumer uncertainty of thequality of the new product. Neither the cost structureof the incumbent or entrant is known and no data areavailable on the temporal pattern of the revelation ofthe entrant’s quality information. These difficulties arenot unique to our model. In fact, any rigorous testing



Table 6 Results from Experiment 1

Possible Explanations for Delayed ResponseMean Likelihood

(Standard Deviation)

(i) There is incumbent inertia—They react slowly. 21.58 (14.01)(ii) Market growth rate is high. 32.07 (19.61)(iii) Reaction may indicate entrant’s quality. 70.24 (21.72)(iv) Entrant is not viewed as a threat. 37.32 (17.21)(v) Market is not important to the incumbent. 26.71 (15.88)(vi) Incumbent’s capacity utilization is high. 51.70 (15.41)(vi) Customer switching costs are high. 52.79 (19.12)

of any theory based on asymmetric information facesthe same set of limitations.

In an attempt to test the proposed theory, we con-ducted two experiments. In Experiment 1, we testedfor the plausibility of the rationale proposed in thispaper.19 In addition, Experiment 1 also compared theproposed explanation with the competing explana-tions proposed in the literature. Given the data limi-tations, the appropriate way to test our model was tobegin by testing (a) the face validity of the model and(b) by comparing the explanatory “power” for the pro-posed explanation relative to others. We did this byproviding decision makers with information aboutconsumers’ quality uncertainty and the timing of qual-ity revelation. The respondents were asked to conjec-ture about the most likely explanation accounting fora firm’s delayed response. Specifically, we tested ourexplanation relative to the explanations proposed byRobinson (1988) and Bowman and Gatignon (1995).Experiment 2 constituted a more direct test of the be-havioral underpinning of our model.

4.1. Experiment 1

Subjects. The subjects were 81 full-time MBA andevening MBA students enrolled in a marketing com-munications class at a private university on the EastCoast. The years of work experience of the subjectsranged from three to six years. Subjects were asked totake part in a marketing decision study. They wereasked to read a scenario that described a decision madeby a firm and then were given a list of potential posthoc reasons as to why the decision was made by thefirm. Subjects were asked to indicate the likelihood thatthe decision was made for the explanations providedto them.

Subjects were told that a firm Oldpro, a subsidiaryof Consolidated Industries, was in the business ofmanufacturing and selling heavy diesel engines. Old-pro was an established and well-respected firm. A yearago, a firm Gamma entered the diesel engine marketand introduced a new product to compete against Old-pro. Further, subjects were informed that Gamma’s

19We thank the acting editor, Rajiv Lal, for suggesting this experi-ment. Though this experiment was not the first conducted chrono-logically, we report it as Experiment 1 for logical consistency.

product was superior in quality relative to Oldpro’sproduct. Oldpro had to make a decision on how torespond to Gamma’s introduction. Subjects were thentold that Oldpro decided not to respond immediatelyto Gamma’s new launch—they waited for one yearand then reduced their prices.

Subjects were provided with a total of seven expla-nations, six of which were hypothesized in the litera-ture as explanations for delayed competitive responses(Bowman and Gatignon 1995; Robinson 1988). Subjectswere instructed to read all the explanations before re-sponding to the question “How likely is it that Old-pro’s management made the decision for the reasonlisted?” on a 100-point scale anchored between not atall likely to very likely. The explanations in the ordergiven to the subjects were: (i) There is inertia in Old-pro’s management—they respond slowly; (ii) The mar-ket is growing at a very high rate; (iii) If Oldpro im-mediately reduced their prices, customers would inferthat Gamma’s product was of high quality; (iv) Oldprodoes nor perceive Gamma to be a threat; (v) The dieselengine market is not very important to Consolidated;(vi) Oldpro’s capacity utilization is high; and (vii) It isvery expensive for customers to switch to the newtechnology.

Results and Discussions. Table 6 summarizes themeans and standard deviations of the responses for theseven explanations provided to the subjects. As can beseen, the subjects judged the delayed reaction of re-ducing prices by the incumbent to have occurred mostlikely because an immediate reaction would have in-dicated the entrant’s quality to the consumers. Theonly other statistically significant explanations for the



Table 7 Results from Experiment 2

Entrant’s Mean Quality Rating(Standard Deviation)

Incumbent’s Price-BasedDefensive Reaction Graduate Subjects Undergraduate Subjects

(i) Price decrease 65.36 (14.61) 64.04 (16.47)(ii) No price change 52.80 (4.07) 53.72 (5.83)(iii) Price increase 47.24 (15.32) 46.66 (15.91)

delayed reaction by the incumbent were those relatedto consumer switching costs and the incumbent’s highcapacity utilization. We believe that these results pro-vide strong evidence that the proposed explanationhas high face validity relative to the alternative expla-nations provided in the literature. Furthermore, the“explanatory power” of the proposed theory wasfound to be satisfactory.

4.2. Experiment 2In Experiment 1, we tested for the face validity of theproposed model. In addition, we demonstrated that,relative to the competing explanations in the literature,the proposed explanation for delayed responses by theincumbent was observed to be the most intuitively ap-pealing. As a further verification of the theory, in thisexperiment we tested a behavioral assumption under-lying the theory. Recall that, in the signal-jammingequilibrium, the incumbent adopts the same pricingstrategy whether he faces a high- or a low-quality en-trant. Such an equilibrium is supported by the consum-ers’ (off-equilibrium) belief that immediate reaction interms of a sharp price cut by the incumbent wouldmean that the entrant’s quality is high. In Experiment2, we verify whether or not an incumbent’s responseto a new product entry with respect to a change inprice impacts consumers’ quality perceptions of theentrant.

Subjects. Two pools of subjects were used. Thefirst set comprised full-time MBA and evening MBAstudents enrolled in a product management class. Thesecond set comprised undergraduate students enrolledin a marketing management class. The subjects wereasked to participate in a experiment pertaining to apurchase decision task. Seventy-six graduate studentsand 65 undergraduate students agreed to participatein the experiment.

Methodology. A single factor between-subjectsdesign (price change) with three levels was employed.The subjects were asked to assume the role of pur-chasing agents in an organization. Specifically, theywere told that their job involved selecting suppliers forindustrial components. Next, they were presentedwith the purchase scenario. The scenario stated thatthey had been buying a component from supplier X.

Further, supplier X’s quality had been rated by thepurchasing department to be 50 on a 100-point scale(where 100 denoted excellent quality and 0 denoted verypoor quality). Supplier X had been charging the firm$1,000 per component. The subjects were then told thata supplier Y was entering the market with a competi-tive component. The purchasing department wouldhave an opportunity to choose between the two sup-pliers at the next purchase occasion. Finally, subjectswere told that they had just received a new price listfrom the incumbent X. The manipulation involved thechange in X’s price: either a decrease to $700, an in-crease to $1,300, or no change at $1,000.

Based on the information provided in the scenario,the subjects were asked to state their quality percep-tions of the new entrant on a 100-point scale (100 4

excellent quality; 0 4 very poor quality). They were alsoasked an open-ended question to explain why theythought the incumbent firm had responded by chang-ing prices.

Results and Discussion. We examined the impactof price response by the incumbent on the quality per-ceptions of the entrant. The results were consistentwith the prediction that, relative to a price increase orno price change, a price decrease by the incumbent willlead to more positive evaluations of the entrant’s qual-ity. The results are summarized in Table 7. The resultsfor the undergraduates correspond very closely tothose found for the graduate subjects. For the graduatepool, subjects who were given the incumbent price de-crease condition judged the quality of the entrant morefavorably (Q 4 65.36) than the subjects who weregiven the incumbent price increase condition (Q 4

47.24; F 4 12.38; p , 0.01) or the subjects who were



given the incumbent no change condition (Q 4 52.80;F 4 27.67; p , 0.01). Similarly, for the undergraduatepool, the subjects exposed to the incumbent price de-crease condition rated the entrant’s quality more fa-vorably (Q 4 64.05) than the subjects who were ex-posed to the incumbent price increase condition (Q 4

46.66; F 4 4.96; p , 0.05) or the subjects who wereexposed to the incumbent no change condition (Q 4

53.72; F 4 15.08; p , 0.01).We also examined the responses to the open-ended

questions to confirm whether the subjects interpretedthe competitive responses as revelation of private in-formation held by the incumbent regarding the qualityof the new entrant. By and large, the stated rationalesprovided confirmatory evidence about the proposedtheory. The results are consistent with the notion thatcompetitive actions by an incumbent to new productentries lead to quality inferences about the entrant.Specifically, as compared with price increases or noprice changes, price decreases by the incumbent resultin higher quality perceptions of the entrant.

5. ConclusionsResponding to new product introductions is one of themajor strategic issues in marketing. Response time bycompetitors is an important component of that strat-egy. Though most normative models have implicitlyassumed or explicitly advocated quick competitive re-actions (Hauser and Shugan 1983; Kumar andSudarshan 1988; Porter 1985), a number of empiricalstudies have found that defensive reactions are oftendelayed (Robinson 1988; Bowman and Gatignon 1995).

In this paper, we provide a rationale as to why adelayed reaction may be the optimal strategy for anincumbent firm. Previous explanations have suggestedthat delayed responses result from either managerialperceptions of a lack of potential threat from newproduct introductions or a lack of managerial compe-tence to respond quickly. We suggest that, under cer-tain conditions, a delayed response may be an optimalor efficient strategy when there is uncertainty about theentrant’s quality. Succinctly, an immediate reaction inthe form of a lower price by the incumbent firm maycause consumers to believe that the entrant’s productquality is high. Therefore, an incumbent may be better

off by delaying the price response until consumerslearn the quality of the entrant’s product over timethrough experience and word of mouth. We findstrong experimental evidence supporting the under-lying premise and explanation of our analysis.

The literature in marketing strategy has traditionallyfocused on either the impact of marketing actions onconsumers or the impact of the strategy on competitivereactions (Gatignon, Anderson, and Helsen 1989;Hanssens 1980). In this paper, we highlight the impor-tance of considering both the competitors and consum-ers simultaneously in examining the incumbent firm’soptimal reaction strategy. This approach becomes ex-tremely important when consumers are able to observecompetitive actions or reactions. We acknowledge thatsome reactions may be unobservable (e.g., trade pro-motions) to consumers but believe that most actionsare detectable to both the competitors and consumers.

The managerial implications of this paper is thatwell-established incumbent firms should be cautiousin the implementation of their defensive responses tonew product introductions of uncertain quality bycompetitors. Of particular concern are situationswhere the reactions are easily observable by consum-ers. A strong reaction may suggest that the incumbenttakes the competitive threat seriously, leading con-sumers to believe in the quality of the competitor’sproduct.

We have shown that when the entrant uses price tosignal her quality, under certain conditions, it may beoptimal for the incumbent not to react aggressively inthe first period.20 The entrant can use other signals aswell. In addition to price,21 the entrant has access toother signaling instruments. For example, advertising(Nelson 1974; Milgrom and Roberts 1986), umbrellabranding (Wernerfelt 1988), retailer reputation (Chuand Chu 1994), product line selection (Balachanderand Srinivasan 1994), product upgrades(Padmanabhan, Rajiv, and Srinivasan 1997), and

20Another explanation for the delayed reaction is that an incumbentmay be uncertain about the entrant’s financial commitment/re-sources. This issue needs further investigation. We thank ProfessorBirger Wernerfelt for this observation.21See Srinivasan (1991), Desai and Srinivasan (1995), andBalachander and Srinivasan (1998) for other marketing analyticalmodels where price is the only signal instrument.



money-back guarantees (Moorthy and Srinivasan1995) can also serve as signaling mechanisms for en-trants. In future research work, we hope to examinethe impact of alternate signaling instruments in deter-mining competitive reactions.22

AppendixProof of Lemma 1. Consider first the case when qE , qI. In this case,the demand functions for the entrant and the incumbent, for a givenset of prices pI and pE, are given by Equations (T1.2) and (T1.1),respectively. It follows that

]D p 1 p pE I E E4 ` . 0, (A.1)2 2]q (q 1 q ) qE I E E

as pE , pI for the entrant’s product to be undominated. Similarly,

]D p 1 pI E I4 , 0. (A.2)2]q (q 1 q )E I E

Now consider the case when qE . qI. In this case, the demand func-tions for the entrant and the incumbent, for a given set of prices pI

and pE, are given by Equations (T1.4) and (T1.3), respectively. It fol-lows that

]D p 1 pE E I4 . 0, (A.3)2]q (q 1 q )E I E

as pE . pI for the incumbent’s product to be undominated. Similarly,

]D p 1 pI E I4 1 , 0. (A.4)2]q (q 1 q )E I E

Proof of Lemma 2. Under monopoly, the demand function facingfirm I is given by (p) 4 1 1 (p/qI), so that the incumbent’s profitPEDI

function is given by

2p q 1 p 1 c q ` p cI I I I I I IPEP 4 , (A.5)I qI

PE]P IG [ q 1 2p ` c 4 0. (A.6)I I I]pI

G Solving (A.6) in pI yields the expression for the optimal pre-entryprice of the incumbent. ▫

22The authors are listed in alphabetical order and contributed equallyto the paper. We thank the acting editor, Rajiv Lal, the editor, RickStaelin, and three anonymous reviewers of this journal for their com-ments. We thank the seminar participants at HKUST, Indian Insti-tute of Management at Calcutta, University of Chicago, UCLA, andUC at Berkeley for their comments. An earlier version of this workwas presented at the Marketing Science Conference at Sydney. Thiswork was partly supported by the Beatrice Companies Faculty Re-search Fund (at the GSB, University of Chicago) to the second au-thor. The usual disclaimer applies.

Proof of Proposition 1. The price competition between the in-cumbent and the entrant when qE , qI is given by the followingprogram:

p 1 pI EP1: p* [ argmax P (p , p ) [ (p 1 c ) 1 1 , (A.7)I I I E I I 3 4q 1 qp I EI

q p 1 q pE I I Ep* [ argmax P (p , p ) [ (p 1 c ) . (A.8)E E I E E E 3 4q (q 1 q )p E I EE

The reaction functions for the incumbent and the entrant in this caseare given by:

]PI [ 2p 1 q ` q 1 p 1 c 4 0, (A.9)I I E E I]pI

]PE [ 2q p 1 q p 1 c q 4 0. (A.10)I E E I E I]pE

Solving the reaction functions simultaneously for pI and pE yields theBertrand-Nash price equilibrium, viz. Equations (T3.1) and(T3.2). ▫

Proof of Proposition 2. The price competition between the in-cumbent and the entrant when qE :mt qI is given by the followingprogram:

q p 1 q pI E E IP2: p* [ argmax P (p , p ) [ (p 1 c ) , (A.11)I I I E I I 3 4q (q 1 q )p I E II

p 1 pE Ip* [ argmax P (p , p ) [ (p 1 c ) 1 1 . (A.12)E E I E E E 3 4q 1 qp E IE

The reaction functions for the incumbent and the entrant in this caseare given by

]PI [ 2q p 1 q p 1 c q 4 0, (A.13)E I I E I E]pI

]PE [ 2p 1 q ` q 1 p 1 c 4 0. (A.14)E E I I E]pE

Solving the reaction functions simultaneously for pI and pE yields theBertrand-Nash price equilibrium, viz. Equations (T3.3) and(T3.4). ▫

Proof of Proposition 3. The optimal pricing strategy for theincumbent in the pre-entry period is given by

q ` cI IPEp 4 , (A.15)I 2

where PE denotes the pre-entry period. In the post-entry period,when consumers know the quality of the entrant’s product, the op-timal pricing strategy of the incumbent is given by Equation (T3.3)if qE . qI and by Equation (T3.1) if qI . qE. We first formally showthat the incumbent’s post-entry price is less than the incumbent’spre-entry price.

First, consider the case when qE . qI. In this case,



q ` c 2q c ` q (q 1 q ` c )I I E I I E I EPEp 1 p* 4 1I I 2 4q 1 qE I

q [2(q 1 c ) ` (q 1 c )]I E E I I4 . 0, (A.16)

2(4q 1 q )E I

as qE . cE and qI . cI. Note that qE is the highest consumer valuationfor the entrant’s product (corresponding to h 4 1) and hence qE .

pE . cE. By a similar logic, qI . pI . cI .Similarly, when qE , qI, as qE . cE and qI . cI, we have

q ` c 2q (q 1 q ) ` q (2c ` c )I I I I E I I EPEp 1 p* 4 1I I 2 4q 1 qI E

2q (q 1 c ) ` q (q 1 c )I E E E I I4 . 0, (A.17)

2(4q 1 q )E I

▫

Proof of Proposition 4. The optimal profit function of the H-typeentrant, when her perceived quality is q̃E, can be written as

H H,* H H H,** *P (q̃ ) 4 [p (q̃ ) 1 c ] 2 D [q̃ , q , p (q̃ ), p*(q̃ )], (A.18)E E E E E E E I E E I E

where and are the optimal prices of the H-type entrant andH,*p p*E I

the incumbent (as given in Proposition 1 when qE , qI and Propo-sition 2 when qE . qI).

Now, by Envelope Theorem (Takayama 1988), we get

H H.* H* *dP [q̃ , p (q̃ ), p*(q̃ )] ]PE E E E I E E4 sign3 4 3 4dq̃ ]q̃E E

H*]DE4 sign . 0. (by Lemma 2) 19)3 4]q̃E

G From (A.19), it follows that the profit of the H-type entrant isincreasing in q̃E. ▫

Proof of Proposition 5. Note that at the undistorted price of theH-type entrant, any marginal increase in the entrant’s price hurts theL-type’s profit while it does not result in any first-order loss for theH-type. Further, as we show below, at any price above the optimal(undistorted price of the H-type entrant, price increase causes greatermarginal loss to the L-type than the H-type entrant; price increasecauses greater marginal loss to the L-type than the H-type entrant;this guarantees that “single crossing” or sorting condition issatisfied.

Let us first consider the case when so that the ex-H Lq . q . q ,E E I

pected quality of the entrant (based on prior beliefs, q) is greaterthan incumbent’s quality, i.e., q̃E . qI. Note that to consider the mar-ginal impact on the entrant’s profit of increase in (pE), we have toconsider both the direct effect of pE and the indirect effect throughpI(PE). Substituting for pI(pE) from (A.13) in (A.12), we obtain theexpression for entrant’s profit as a function of pE alone. Differenti-ating w.r.t. pE, it can be shown that

]P (q̃ , p ) q̃ (2q̃ 1 q 1 c ) 1 2p (2q̃ ` q ) ` c (2q̃ ` q )E E I E E I I E E I E E I4 ,

]p 2q̃ (q̃ 1 q )E E E I

(A.20)

and

2] P (q̃ , p ) 2q̃ ` q )E E I E I4 . 0. (A.21)

]p ]c 2q̃ (q̃ 1 q )E E E E I

which implies that

H H L L]P (q̃ , p , c ) ]q̃ (q̃ , p , c )E E I E E E I E1 . 0. (A.22)

]p ]pE E

But for any upward price distortion beyond the undistorted price ofthe H-type incumbent, profits decrease both for the H-type and theL-type entrant. This, together with (A.22), implies that

H H L L]P (q̃ , p , c ) ]P (q̃ , p , c )E E I E E E I E, . (A.23)) ) ) )]p ]pE E

and since both and are of the same sign (i.e., neg-H L]P /]p ]P /]pE E E E

ative), we have

L L H H]P (q̃ , p , c ) ]P (q̃ , p , c ) *E E I E E E I E HG . for ∀ p > p . (A.24)E E@]p ]pE E

Now consider the case qI . or equivalently qI q̃E. SubstitutingH Lq q ,E E

for pI(PE) from (A.9) in (A.8), we obtain the expression for entrant’sprofit as a function of pE alone. Differentiating w.r.t. pE, it can beshown that

]P (q̃ , p ) q̃ (q̃ ` c ) 1 p̃ ) 1 2p (2q 1 q̃ ) ` c (2q 1 q̃ )E E I E I I E E I E E I E4 ,

]p 2q̃ (q 1 q̃ )E E I E

(A.25)

and

2] P (q̃ , p ) 2q 1 q̃ )E E I I E4 . 0. (A.26)

]p ]c 2q̃ (q 1 q̃ )E E E I E

which, following similar logic as above, implies that

L L H H]P (q̃ , p , c ) ]P (q̃ , p , c ) *E E I E E E I E HG . 1 for ∀ p > p . (A.27)E E@]p ]pE E

G From Equations (A.24) and (A.27), it follows that the L-type en-trant incurs a higher marginal loss (resulting from an upward pricedistortion) than the H-type entrant. ▫

Proof of Proposition 6. The optimal profit function of the in-cumbent, when the perceived quality of the H-type entrant is q̃E, canbe written as

H,*P*(q̃ ) 4 [p*(q̃ ) 1 c ] 2 D*[q̃ , q , p (q̃ ), p*(q̃ )]. (A.28)I E I E I I E I E E I E

where and are the optimal prices of the H-type entrant andH,*p p*E I

the incumbent (as given in Proposition 1 when qE , qI and Propo-sition 2 when qE . qI).

Now, by Envelope Theorem (Takayama 1988), we get

H.*dP *[q̃ , p (q̃ ), p*(q̃ )] ]P*I E E E I E IG sign 4 sign3 4 3 4dq̃ ]q̃E E

]D*I4 sign , 0. (by Lemma 2) (A.29)3 4]q̃E



G From (A29), it follows that profit of the incumbent is decreasingin q̃E.

The same logic holds in the case of the L-type entrant as well. Weomit details for brevity. ▫

Proof of Proposition 7. Consider first the case when .H Lq . qE E

qI, so that q̃E . qI. In this case, from Equation (A20), we have

L H L]P ]P q̃ (2q̃ 1 q 1 c ) 1 2p (2q̃ ` q ) ` c (2q̃ ` q )E E E E I I E E I E E I4 ,@ H]p ]p q̃ (2q̃ 1 q 1 c ) 1 2p (2q̃ ` q ) ` c (2q̃ ` q )E E E E I I E E I E E I

(A.30)

L H]P ]PE E] 3 @ 4]p ]pE EG 4

]pE

H L2(c 1 c )(2q̃ ` q )E E E I1 , 0.H 2[q̃ (2q̃ 1 q 1 c ) 1 2p (2q̃ ` q ) ` c (2q̃ ` q )]E E I I E E I E E I

(A.31)

G This implies that the H-type’s marginal ability to separate de-creases at higher prices of the H-type entrant. Now, as noted earlier,the reaction functions of the incumbent and the entrant are upwardsloping in their respective competitive prices because of strategiccomplement effect (Fudenberg and Tirole 1984; Bulow,Geanakoplos, and Klemperer 1985). This implies that by raising hisprice, the incumbent forces the H-type entrant to raise her price butat this level of H-type’s price, her marginal ability to separate islower. Thus, increasing pI implies reduced marginal ability to sepa-rate for the H-type.

Similarly, in the case when qI . , or equivalently qI . q̃E,H Lq . qE E

from Equation (A.25), we have

L H]P ]PE E] 3 @ 4]p ]pE EG 4

]pE

H L2(c 1 c )(2q ` q̃ )E E I E1 , 0.H 2[q̃ (q ` c 1 q̃ ) 1 2p (2q 1 q̃ ) ` c (2q 1 q̃ )]E I I E E I E E I E

(A.32)

G By a similar logic as above, it follows that increasing pI impliesreduced marginal ability to separate for the H-type. ▫

Proof of Proposition 8. Consider first the case when qI . qE. LetpI be any given price of the incumbent. Now, the options availableto the L-type entrant are: (1) to select her complete-information price,

(for the given pI), and be revealed as the L-type in which caseL,*pE

her perceived quality is ; or (2) to mimic the H-type by selectingLqE

the H-type’s complete-information price, (for the given pI), andH,*pE

“pool” in which case, since both the entrant types select the sameprice, (for the given pI), her perceived quality is q̃E.H,*pE

Now, the L-type’s profit when it “pools” with the H-type by se-lecting (for the given pI) is given byH,*pE

H,*q̃ p 1 q pE I I EL,q H,* HP (p ) 4 (p 1 c ) , (A.33)E I E E 3 4q̃ (q 1 q̃ )E I E

while her profit when she selects (for the given pI) and is revealedL,*pE

as the L-type is given by

L L,*q p 1 q pE I I EL,L L,* HP (p ) 4 (p 1 c ) . (A.34)E I E E 3 4L Lq (q 1 q )E I E

Let

H,*q̃ p 1 q pE I I EL,q L,L H,* HD(p ) 4 P (p ) 1 P (p ) 4 (p 1 c )I E I E I E E 3 4q̃ (q 1 q̃ )E I E

L L,*q p 1 q pE I I EL,* H1 (p 1 c ) . (A.35)E E 3 4L Lq (q 1 q )E I E

Note that D(pI) measures the L-type’s gains from mimicking the H-type and hence measures the L-type’s incentive to “pool” on quality.

H,* L L,* L]D p 1 c p 1 cE E E EG 4 1 L]p q 1 q̃ q 1 qI I E I E

H,* L L,* L Lp (q 1 q ) 1 p (q 1 q̃ ) 1 c (q̃ 1 q )E I E E I E E E E4 . (A.36)L(q 1 q̃ )(q 1 q )I E I E

Note that q̃E . . Let q̃E 4 ` d with d . 0.L Lq qE E

H,* L,* L H,* L L,* L L]D q (p 1 p ) 1 q p ` (q ` d)p 1 c (q̃ 1 q )I E E E E E E E E EG 4 ,L]q (q 1 q̃ )(q 1 q )I I E I E

(A.37)

L H,* L,* L,* L]D (q 1 q )(p 1 p ) ` d(p 1 c )I E E E E EG 4 . 0, (A.38)L]q (q 1 q̃ )(q 1 q )I I E I E

since qI . , , , and d . 0.L H,* L,* L,* Lq p . p p . cE E E E E

Thus, the L-type’s incentive to “pool” on quality increases withpI. ▫

Proof of Lemma 3. The mimicking constraint in Program P3,Equation (T4.2), is given by

H Hq p 1 q pE I I EH L L,* L(p 1 c ) # [p (p ) 1 c ]E E E I E3 4H Hq (q 1 q )E I E

L L,*q p 1 q p (p )E I I E I2 , (A.39)3 4Lq̃ (q 1 q )E I E

where (pI) is the complete information reaction function of theL,*pE

L-type entrant and from Equation (3) is given by

L Lq p ` c qE I E IL,*p (p ) 4 . (A.40)E I 2qI

Substituting (pI) in the Equation (T4.2), we obtain for the right-L,*pE

hand side of the mimicking constraint, viz., the L-type’s profit undercomplete information reaction function, (pI), asL,*PE

L Lq p ` c qE I E ILq p 1 qE I I 1 2L L 2qq p ` c q IE I E I L1 c 2E3 4 L2q q̃ (q 1 q )I E I E3 4L L 2[q p 1 c q ]E I E I

4 , (A.41)L L4q q (q 1 q )I E I E

which is independent of . For notational simplicity, we denoteHpE

(pI) by k. The Lagrangean for Program P3 is given byL,*PE



H Hq p 1 q pE I I EH HL 4 (p 1 c )E E 3 4H Hq (q 1 q )E I E

H Hq p 1 q pE I I EH L` l (p 1 c ) 1 k . (A.42)I E E3 3 4 4H Hq (q 1 q )E I E

The Kuhn-Tucker conditions are

]L H H[ p q (1 ` l ) 1 2q p (1 ` l )I E 1 I E 1H]pE

H L` q (c ` l c ) 4 0, (A.43)I E 1 E

]L H L H H H H[ (p 1 c )(q p 1 q p ) 1 kq (q 1 q ) 4 0, (A.44)E E E I I E E I E]l1

]L ]LH Hp 4 0, l 4 0, p $ 0, l # 0. (A.45)E 1 E 1H]p ]lE 1

At the least-cost quality separation, the mimicking constraint of theL-type entrant is binding, which implies that lI , 0. Solving (A.43)for , we getHpE

H H Lp q (1 ` l ) ` q (c ` l c )I E 1 I E 1 EHp 4 . (A.46)E 2q (1 ` l )I 1

Further, the second-order optimality condition requires that thesecond-derivative of the Lagrangean be negative. Thus

2] L[ 12q (1 ` l ) , 0 ⇔ l . 11. (A.47)2 I 1 1H]pE

Substituting from (A.46) in (A.44), we getHpE

2 H L 2 H Hl [(q p 1 c q ) 1 4kq q (q 1 q )]1 E I E I E I I E

H L 2 H H` 2l [(q p 1 c q ) 1 4kq q (q 1 q )]1 E I E I E I I E

H L 2 H H H H H H`[2c c q 1 (q p ` c q )(c q 1 q p ) 1 4kq q (q 1 q )E E I E I E I E I E I E I I E

H L1 2p q q c ] 4 0, (A.48)I I E E

which is a quadratic equation in lI of the form ` bl1 ` c 4 0,2al1

where

H L 2 H Ha 4 2b 4 (q p 1 c q ) 1 4kq q (q 1 q ), (A.49)E I E I E I I E

and

H L 2 H H H Hc 4 2c c q 1 (q p ` c q )(c q 1 q p )E E I E I E I E I E I

H H H L1 4kq q (q 1 q ) 1 2p q q c . (A.50)E I I E I I E E

Solving for lI, using the formula

21b 5 b 1 4ac! a 1 cl 4 4 1 1 5 (•• b 4 2a), (A.51)1 •!2a a

we get

l 4 11 5I

H L 2 H H H H H L 2 H L(q p 1 c q ) ` (q p ` c q )(c q 1 q p ) 1 2c c q ` 2p q q cE I E I E I E I E I E I E E I I I E E.H L 2 H H! (q p 1 c q ) 1 4kq q (q 1 q )E I E I E I I E

(A.52)

But since lI . 11, to be consistent with the second-order condition,the desired expression for lI is

l 4 11 `I

H L 2 H H H H H L 2 H L(q p 1 c q ) ` t(q p ` c q )(c q 1 q p ) 1 2c c q ` 2p q q cE I E I E I E I E I E I E E I I I E E .H L 2 H H! (q p 1 c q ) 1 4kq q (q 1 q )E I E I E I I E

(A.53)▫

Proof of Lemma 4. Equation (A.53) gives the expression for l1(pI).Differentiating l1(•) with respect to pI, we have

]l14 1

]pI

H H L H Lq q (c 1 c )[p q 1 q c ]I E E E I E I E , 0. (A.54)2 22 H H L H H L 3/2{p q 1 2p q q c ` q [4kq (q 1 q ) ` q c ]}I E I E I E I E E I I E

This is so due to the following reason: Note that from Equations(A.40) and (A.41), . 0, otherwise the L-type entrant’sL Lp q 1 q cI E I E

equilibrium demand as well as per unit contribution margin undercomplete information is negative. Since , it follows thatH Lq . qE E

. 0. This completes the proof of the first claim.H Lp q 1 q cI E I E

Now, under complete information when qI . . , the H-typeH Lq qE E

entrant’s reaction function is given by Equation (A.10), i.e.,

H Hq p ` c qE I E IH,*p (p ) 4 , (A.55)E I 2qI

so that

H,* H]p qE E4 .

]p 2qI I

Furthermore, from Equation (A.46), the H-type entrant’s least-costseparating reaction function under quality signaling is given by

H H Lq p (1 ` l ) ` q (c ` l c )QS E I 1 I E 1 EHp (p ) 4 [ n(p , l (p )), (A.56)E I I 1 I2q (1 ` l )I 1

so that

QSH]p ]n ]n ]lE 14 ` 2 . (A.57)

]p ]p ]l ]pI I 1 I

Now, we have

H]n qE4 , (A.58)

]p 2qI I

H L]n c 1 cE E4 1 , 0, (A.59)

]l 2(1 ` l )1 1

and Equation (A.54) gives the expression for ]l1/]pI. Thus, usingEquations (A.54)–(A.59), we have



QSH H]p ]p ,* ]n ]lE E 11 4 2 4

]p ]p ]l ]pI I 1 I

H H L 2 H Lq q (c 1 c ) [p q 1 q c ]I E E I E I EE2 22 H H L H H L 3/22(1 ` l ){p q 1 2p q q c ` q [4kq (q 1 q ) ` q c ]}1 I E I E I E I E E I I E

. 0.(A.60)

▫

Proofs of Lemma 5 and Proposition 9. We first derive the re-action function of the incumbent under signal-jamming for any an-ticipated price of the H-type entrant. (Of course, in the equilib-HpE

rium, this will coincide with the actual price selected by the H-type.)The Lagrangean corresponding to P38 is given by

H 2 Hp (q 1 q̃ ` p ` c ) 1 p 1 c (q 1 q̃ ` p )I I E E I I I I E EL 4q 1 q̃I E

22 H H 2 H 2 2 L L Hp q 1 2p q c q c (1 ` 2l ) 1 l q c (c 1 2c )I E I I E I E 1 1 I E E E` l `2 3 H H H 24q (q 1 q ) 4q q (q 1 q )(1 ` l )I I E E I I E 1

2H H H H Hq̃ p (p 1 c ) 1 q p ` q c pE I E E I E I E E1 .4q̃ (q 1 q̃ )E I E

(A.61)

The Kuhn-Tucker conditions are

H H H]L q 1 q̃ ` p ` c 1 2p 1 l (p 1 c )I E E I I 2 E E4

]p q 1 q̃I I E

H Hl [p q 1 q c ]2 I E I E` 4 0, (A.62)H2q (q 1 q )I I E

2 H H]L p q 1 2p q cI E I I E4 H]l 4q (q 1 q )2 I I E

22 H 2 2 L L Hq c (1 ` 2l ) 1 l q c (c 1 2c )I E 1 1 I E E E` H H 24q q (q 1 q )(1 ` l )E I I E 1

2H H H H Hq̃ p (p 1 c ) 1 q p ` q c pE I E E I E I E E1 4 0, (A.63)

q̃ (q 1 q̃ )E I E

]L ]Lp 4 0, l 4 0, p $ 0, l # 0. (A.64)I 2 I 2]p ]lI 2

At the most efficient (i.e., at least cost to the incumbent), the signal-jamming constraint of the H-type is binding, which implies that l2

, 0. Solving (A.62) for pI, we get the signal-jamming reaction func-tion of the incumbent as

H2p 1 c ` q̃ 1 c 1 qI E E I I

H Hq (q 1 q̃ ) cE I E EH1 l ` p ` 4 0. (A.65)2 E3 4H2q (q 1 q ) 2I I E

Furthermore, the second-order optimality condition requires that thesecond-derivative of the Lagrangean be negative. Thus,

2 H] L 2 l q2 E4 1 `2 H]p q 1 q̃ 2q (q 1 q )I I E I I E

H4q (q 1 q )I I E, 0 ⇔ l , . (A.66)2 Hq (q 1 q̃ )E I E

Note that since the right-hand side of (A.66) is a positive numberand the Lagrangean multiplier l2 , 0, the second-order condition isalways satisfied at the maximum.

The signal-jamming equilibrium prices are the pair of prices ^pI,pE& that simultaneously satisfy the reaction functions (A.46) and(A.65). (Note that using the general form of the Implicit FunctionTheorem (Simon and Blume 1994, pp. 350–358), it can be shown thatsuch a solution exists.)

This signal-jamming equilibrium is supported by the off-equilibrium beliefs pI ? ⇒ q 4 1 and/or pE ? ⇒ q 4 0. NoteSJ SJp pI E

that we need to consider the out-of-equilibrium belief for any uni-lateral deviation by either the incumbent or the entrant. In ourmodel, firms select prices simultaneously and noncooperatively.Hence, joint or coordinated defections are not relevant and, thus, thespecification of our beliefs. Note that these off-equilibrium beliefssatisfy intuitive criterion (Cho and Kreps, 1987). For defection tohigher than signal-jamming prices by the incumbent intuitive crite-rion does not impose any restriction. Neither the incumbent facinga true high-type entrant nor the incumbent facing the true low-typeentrant will defect to such higher prices. A similar reasoning holdsfor upward defection for either type entrant (technical details havebeen omitted for brevity and are available from the authors onrequest).

Now consider deviations below the signal-jamming prices. Notethat is above the complete-information price of the incumbentSJpI

(either when entrant is H- or L-type). Hence, under the most favor-able consumer beliefs (i.e., it is the L-type entrant), by deviatingdownwards, the incumbent can increase his profits (both when theentrant is H- and L-type). Thus, intuitive criterion cannot refine thisoff-equilibrium belief. Similarly, note that is higher than the com-SJpE

plete information price of both the H- and L-type entrants. Hence,under the most favorable consumer beliefs (i.e., it is the H-type en-trant), by deviating downwards, both the H- and L-type entrants canincrease their profits. Thus, again in this case, the intuitive criterioncannot refine this off-equilibrium belief.

In summary, the beliefs supporting the focal signal-jamming equi-librium are sustained by the intuitive criterion. Any equilibria en-tailing higher than the signal-jamming prices for either the incum-bent or the entrant can be ruled out by application of elimination ofdominated strategies (Moulin 1979). Now consider any price lowerthan the signal-jamming equilibrium as a candidate pooling equilib-rium. This can only be sustained with the belief at any other entrant’sprice, the type is low. Now that the incumbent’s price is lower thanthe signal-jamming price, the high-quality entrant can separate atthe signal-jamming price. (Only to prevent this, the incumbentchooses to jam the signal in the first place, as derived in our focalanalysis.) Given such a separation, the high-type will defect, whilethe low-type will not. Therefore, the only “reasonable” belief sup-ported by intuitive criterion is that the entrant’s type is high. Such



a belief, however, overturns the suggested pooling equilibrium. Ex-tending the logic, any pooling equilibria with prices lower than thesignal-jamming equilibrium prices can be eliminated. Thus, we es-tablish that the focal signal-jamming pooling equilibrium is unique.

▫

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