The Equilibrium of B2B e-Marketplaces: Ownership Structures, Market Competition, and

Previous Buyer-Seller Relationships

Kexin Zhao*, Mu Xia, Michael J. Shaw

Department of Business Administration, School of Business, University of Illinois at Urbana-

Champaign, 350 Wohlers Hall, MC-706, Champaign, IL 61820, USA.

{kzhao, mxia, mjshaw@uiuc.edu}

Phone: 1-217-384-6910

Chandrasekar Subramaniam

Department of Business Information Systems and Operations Management, Belk College of

Business, University of North Carolina at Charlotte, 9201 University City Blvd, Charlotte, NC

28223, USA.

{csubrama@email.uncc.edu}

Abstract: B2B e-marketplaces drastically alter the structure of buyer-seller relationships. To

study the equilibrium of a buyer-seller exchange network before and after the emergence of e-

marketplaces, we develop a multiple-person noncooperative game, where rational firms select

optimal interfirm connections and the network is endogenously formed and evolved. We examine

when previous buyer-seller relationships exist, under what conditions both neutral and biased

B2B e-markets will sustain in both the oligopoly market and the oligopsony market. Our analysis

identifies critical success factors for a sustainable e-marketplace. First, low e-market channel

setup costs are critical to attract firms’ participation. Second, the number of buyers and sellers

affects the sustainability of B2B e-markets. For a neutral e-marketplace to survive, high

fragmentation is required on both sides. For a biased e-market, how the number of firms on the

non-owner side influences the e-market equilibrium depends on market competition. Third, in

both the oligopoly market and the oligopsony market, a neutral e-market has similar equilibrium

conditions. By contrast, market competition has a profound impact on the formation of a biased e-

market. The biased e-market formed by the more competitive side is less likely to survive. Finally,

we show that social welfare is improved with the emergence of a neutral e-marketplace, but the

change is ambiguous in a biased B2B e-marketplace case.

*Corresponding author.

- 1 -

Keywords: Economics, game theory, B2B e-marketplaces, ownership structure, market competition

I. Introduction

B2B e-marketplaces match buyers and sellers with automated transactions, lower searching

costs, and increased process effectiveness and efficiency (Bakos 1997; Bakos 1998; Kaplan and

Sawhney 2000). The emergence of such e-marketplaces represents one of the major market

transformations brought about by the proliferation of information technologies (Malone et al.

1987; Grover and Ramanlal 1999). However, despite firms’ enthusiasm in Internet-based B2B e-

marketplaces, the growth of B2B transactions has fallen short of earlier expectations (Digital

Economy 2003, P. 97). Most notably, the shakeout of B2B e-markets during the late 1990s and

early 2000s has spurred skepticism about earlier high expectations. A large number of B2B e-

markets, such as Chemdex.com and Adauction.com, went out of business, while others, including

e-Steel and Covisint, changed their business model from e-market operators to technology service

providers. Nevertheless, there are still hundreds of B2B e-markets that have survived and thrived

(Laseter and Bodily 2004). It is thus intriguing to understand why some e-marketplaces have

survived while others failed and identify critical success factors for a sustainable e-marketplace.

In this paper, we try to answer the question by focusing on the structural dimension of e-

markets (Gosain and Palmer 2004), which refers to the overall pattern of connections between

firms. The structural perspective provides us insights into network stability, when individual firms

strategically establish interorganizational links. The resulting network and firms’ relative position

in it determine their bargaining power and performance. When a B2B e-market reaches

equilibrium, both participating firms and the market operator are willing to keep their existing

connections. This implies the emergence of a sustainable B2B e-market. Otherwise, the e-market

will fall apart and evolve into other business models or exit the market.

We develop a multiple-person non-cooperative game to simulate the endogenous formation of

public B2B e-marketplaces (many-to-many connections). In the model, we describe the overall

network structure as a graph, in which rational and self-interested firms are nodes and their

business relationships are the edges between corresponding nodes. Buyers and sellers select

individual connection channels in the game, and their payoffs are determined by the overall

network structure and their relative positions in it. We study both neutral and biased e-

marketplaces formed in both an oligopoly market and an oligopsony market (Table 1). A neutral

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e-marketplace is owned by an independent intermediary, while a biased one is operated by a

group of buyers or sellers (Yoo, et al. 2005). For the rest of this paper, we focus on buyer-biased

e-marketplaces. The case in which sellers invest in the biased e-marketplace demonstrates similar

properties1. In addition to ownership and market competition structures, we also consider the

impact of previous buyer-seller relationships, as in many cases, firms have had some direct

exchanges before doing business together in e-marketplaces. A B2B e-marketplace can either

bring prior disconnected firms together or substitute for former direct buyer-seller contacts. To

the best of our knowledge, this is the first time in the literature that the process of B2B e-markets

superseding direct buyer-seller networks has been investigated.

Table 1: The Endogenous Formation of B2B e-Marketplaces

Prior Network Structures Posterior Network Structures

A Neutral B2B e-Marketplace

The

Oligopoly

Market

A Buyer-Biased B2B e-Marketplace

A Seller-Biased B2B e-Marketplace

Buyers

Sellers

1 Yoo et al. (2005) also find that biased marketplaces, no matter whether buyer-biased or seller-biased ones, have

similar economic properties.

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A Neutral B2B e-Marketplace

The

Oligopsony

Market

A Buyer-Biased B2B e-Marketplace

A Seller-Biased B2B e-Marketplace

Buyers

Sellers

Our analysis yields several insights on the equilibrium as well as social welfare impacts of B2B

e-marketplaces. First, we recognize that low e-market channel setup costs are critical to attract

firms’ participation. Second, the number of buyers and sellers affects the sustainability of e-

markets. For a neutral e-marketplace to survive, high fragmentation is necessary on both the

buyer side and the seller side. For a biased e-market, how the number of firms on the non-owner

side influences the e-market equilibrium depends upon market competition. For example, in the

oligopsony market, for a buyer-biased market to survive, a sufficient number of sellers are

required. However, in the oligopoly market, the number of sellers has both positive and negative

impacts on the equilibrium of the buyer-biased e-market. On the one hand, with more sellers in

the network, buyers can enjoy more reductions in link costs. On the other hand, the marginal

benefit resulting from enhanced bargaining power decreases. Third, in both the oligopoly market

and the oligopsony market, a neutral e-market has similar equilibrium conditions. By contrast, the

formation of a biased e-market is profoundly influenced by market competition. The biased e-

market formed by the more competitive side (i.e., the buyer group in the oligopoly market and the

seller group in the oligopsony market) is less likely to survive. The reason is that the demand or

supply aggregation can dramatically improve the bargaining power of the previously more

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competitive side, and the other side will react strongly against the formation of such biased e-

marketplaces. Also, the coordination and negotiation costs for splitting the newly generated

surplus among heterogeneous e-market owners may be too high for the e-market to sustain.

Finally, we show that social welfare is improved with the emergence of a neutral e-marketplace,

but the change in social welfare is ambiguous in the biased e-marketplace case.

The rest of our paper is organized as follows. We first review the related literature on network

economics models and B2B e-marketplaces. In Section 3, we present our model and apply it to

study direct buyer-seller networks and to establish pre-e-market equilibrium structures in both the

oligopoly market and the oligopsony market. In Sections 5 and 6, we study the formation of a

neutral B2B e-marketplace and a buyer-biased e-marketplace, respectively. We then discuss the

robustness of our analysis. Finally, we summarize our research contributions and identify future

research opportunities.

II. Literature Review

Extensive studies of network economics provide the theoretical foundation for our paper.

Economists have used the game theoretical approach to model network formation for over a

decade (Aumann and Myerson 1988; Myerson 1991). This line of research suggests that network

structures are important in determining the outcomes of economic and social interactions, such as

bilateral product exchanges and technology adoption (Jackson 2005; Sundararajan 2005).

Previous studies also identify typical network structures and their stability conditions under

various circumstances, such as the star structure and the wheel structure (Bala and Goyal 2000;

Kranton and Minehart 2001). Our model builds upon this knowledge to solve the equilibrium

conditions of B2B e-markets.

While many studies of network economics focus on an abstract network in which players are

homogenous and anonymous (Bala and Goyal 2000), recent developments have begun to examine

networks in more concrete social or economic settings, such as co-author networks and buyer-

seller networks (Jackson and Wolinsky 1996; Kranton and Minehart 2001; Wang and Watts

2003). We focus on a buyer-seller network as a starting position and examine the emergence of an

e-market. Our work is related to Kranton and Minehart (2001) but we consider a few additional

factors. First, we study two competition structures, including the oligopsony market in addition to

the oligopoly market only. Second, we explore the dynamics of the formation of B2B e-

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marketplaces starting from a direct buyer-seller network. While it is agreed that advanced

information technologies stimulate new B2B connections among firms thus transform prior stable

network structures to new ones, the transition has yet to be analyzed in the literature.

Prior electronic markets studies have analyzed the impact of IT on market transformation by

discussing macro trends towards electronic markets, electronic hierarchies, or the “move to the

middle” hypothesis (Malone, et al. 1987; Clemons, et al. 1993), without examining in a micro

context how firms would change their relationships with their trading partners in a network. Our

work offers a more focused examination of the structures of B2B relationships in a digital buyer-

seller network. While previous literature have looked at an individual firm’s choice among

alternative electronic channels (Chang, et al. 2003; Kauffman and Mohtadi 2004), we examine the

resulting network-level conversion.

There are extensive studies analyzing the design and implementation of electronic market

mechanisms (Geoffrion and Krishnan 2003; Anandalingam, et al. 2005). In the present paper, we

assume that a price discovery mechanism has been established; yet transactions only are

conducted between buyers and sellers who are connected. Therefore, firms have to, ex ante,

determine optimal linkage patterns in order to maximize their ex post payoffs from a bilateral

exchange constrained by the network structure.

Yoo et al. (2005) study firms’ participation in both neutral and biased B2B e-marketplaces.

They find that biased e-marketplaces bring a greater surplus to participants than neutral e-markets

do. We also study how ownership structures influence the endogenous formation and equilibrium

of B2B e-markets. The difference is that in our model, there are direct buyer-seller exchanges

before the formation of e-markets. Yoo’s model represents a special case of our model, when an

e-market brings previously unconnected buyers and sellers together.

Kleindorfer and Wu (2003) survey contract structures in both B2B spot markets and long-term

markets in capital-intensive industries. Along the same line of research, Wu and Kleindorfer

(2005) propose a game between one buyer and multiple sellers to study integrated contracting and

spot market options. They characterize market equilibrium conditions and analyze how market

structures affect B2B transactions. While we focus only on B2B spot markets, we confirm that the

market competition structure plays a critical role in determining the stability and efficiency of

buyer-seller exchanges. Our analysis sheds light on the sustainability of a B2B e-market by

- 6 -

focusing on its equilibria under various ownership and market competition structures, when there

have been previous direct buyer-seller exchanges.

III. Model Framework

In this section, we introduce our basic model framework and explain the rationale behind each

of our assumptions. Consider an exchange network consisting of buyers,

and sellers,

m

},,...,1{ , mMiBi ∈ n },...,1{ , nNjS j ∈ . The number of buyers and sellers is

exogenously given in the model. Firms exchange a homogenous product in the network, and each

buyer demands one unit of the product while each seller produces one unit. A buyer has a

reserved valuation, , for the product, and a seller incurs a production cost, . iv jc

3.1 The Two Market Structures

In this paper, we study the emergence of e-marketplaces in both the oligopoly market, i.e. there

are more buyers than sellers, and the oligopsony market, i.e. there are more sellers than buyers.

In the oligopoly market, the demand of the good exceeds the supply, . We normalize

sellers’ production cost to 0; while each buyer has a heterogeneous willingness-to-pay, , that

is independently and identically drawn from a commonly known uniform distribution between 0

and 1. The actual realization of is only known to the buyer himself.

nm >

jc iv

iv iB

In the oligopsony market, the market competition is among sellers, nm < . We assume that

each buyer has the same valuation, 1, for the good, while the seller privately knows his own

production cost . Again, is independently and identically distributed on [0,1] with the

commonly known uniform distribution.

jS

jc jc

In the model, we assume homogeneity of either the sellers’ production costs or the buyers’

reservation values for the side with fewer players, and heterogeneity for the more competitive

side2. When one side has more players, it will face intense competition. Heterogeneity arises as

players on the competitive side differentiate themselves either through improving production

2 We do not consider the special case where the number of buyers equals the number of sellers. In this case, market

competition will only play a trivial role in determining the good allocation in the unit demand market.

- 7 -

efficiency or through various preferences in order to win business. Therefore, we describe two

typical market structures in this way.

3.2 Bilateral Exchange Constrained by the Network Connection

In the network, we limit the bilateral exchange between connected buyers and sellers only,

either via a direct buyer-seller link or via an e-market. In this setting, a business relationship, or a

“link”, is the prerequisite for the bilateral exchange (Wang and Watts 2003). Intuitively, firms

first need to locate potential trading partners and establish certain connections to conduct business

transactions. For example, they may need to directly connect their internal information systems to

facilitate electronic transactions. Or they may choose to go to the same B2B e-market if they

intend to exchange products via an intermediary. Only then can the physical exchange of goods

occur. In this model, we use a graph, , to represent firms and their relationships. Accordingly,

firms within the network are nodes and their business relationships are undirected links,

G

g , in

between. If , it indicates an established connection between buyer and seller , and

the future exchange of good between them is feasible. Otherwise, buyer cannot obtain the

product from seller if . Since the relationship is undirected, .

1=jiSBg iB jS

iB

jS 0=jiSBg

ijji BSSB gg =

We use a second price auction to present the competition between multiple, interconnected

buyers and sellers. Restrictive as they may seem, second price auctions are more general than a

specific auction format—they are similar to Walrasian auctions in which, in the oligopoly market,

sellers hold simultaneous ascending price auctions with the going price being the same across all

sellers. The prices rise and enough buyers drop out for the demand to match supply (Kranton and

Minehart 2001). The oligopsony market case is similar except that all buyers hold the descending-

bid auctions concurrently. As the price decreases from 1, each seller decides whether or not to

drop out of its linked buyers’ auctions. The price changes until enough players on the competing

side exit the auction, so that demand equals supply and the products will be traded. The second

price auction has some desirable features since it leads to efficient product allocation and truth-

telling is a dominant strategy. Efficient products allocation means buyers with highest valuation

will obtain the goods in the oligopoly market, while sellers with lowest production costs will sell

the goods in the oligopsony market.

- 8 -

Overall, the auction mechanism and the network structure jointly determine the final

transactions between buyers and sellers. The auction and the product exchange can only take

place between linked buyers and sellers, which makes the model fundamentally different from a

traditional second price auction. The bilateral exchange constrained by the network connection

also exhibits double-sided network effects (Yoo, et al. 2005). A buyer enjoys positive network

effect as more sellers establish connections with it. Meanwhile, the buyer needs to compete with

other buyers who connect to the same seller.

3.3 Network Equilibrium: Pairwise Stability

One important characteristic of a network structure is that mutual consent is necessary for

establishing a connection between a pair of partners but severing a link needs only a unilateral

decision from either party involved. This is captured in the concept of pairwise stability for a

network equilibrium (Jackson and Wolinsky 1996; Jackson 2003). Pairwise stability implies that

the business relationship in a buyer-seller network has to be mutually beneficial, and this

assumption reflects the fact that “linkage formation inherently requires that not only must a firm

be desirous of forming a linkage, it should also be attractive to potential partners” (Ahuja 2000).

We use the value function, )(Gfπ , to denote the expected payoff of any firm in the network

G. Pairwise stability requires that links in the equilibrium network satisfy:

f

G

versa viceand ),()( then )()( if , allFor )(

)()( and )()( , allFor )(

'''''

'''''

ffffffffff

ffffffffff

gGGgGGGgii

gGGgGGGgi

+>+<∉

−≥−≥∈

ππππ

ππππ

Condition means that for a link to be in the equilibrium network, it has to be beneficial for

firms at both ends of the link to maintain the connection when the network G reaches pairwise

stability. Condition requires that if one firm wants to add an additional link to an equilibrium

network, its target partner will reject the request since its payoff will be worse. Those two

conditions imply that any buyer-seller relationship, , which belongs to a pairwise stable

network, should increase both parties’ expected payoffs or at least leave them the same.

Otherwise, any one of the firms can discontinue the conjunction unilaterally.

)(i

)(ii

g

3.4 Two-stage Game

- 9 -

We use a two-stage game to describe the formation and transition of buyer-seller networks. At

Stage I, firms within the network simultaneously make their connection choices. A firm has

incentive to connect to multiple trading partners in order to have more auction opportunities and

to keep a strong bargaining position in the network. After the first stage, the resulting network

structure is observable to all players. At Stage II, firms know their private information and

compete with each other in the auction constrained by the network structure.

IV. Pre-e-Market Structures: Direct Buyer-Seller Networks

Before the emergence of e-marketplaces, buyers and sellers trade directly. B2B e-markets alter

buyer-seller relationships at both the individual level and the network level (Riggins 1999). In this

paper, we omit the case in which e-markets supersede physical markets without fundamental

structure changes. An excellent discussion about how the Internet affects markets is provided by

Bakos (1998).

In a direct buyer-seller network, we assume that it costs a buyer to build and maintain a

direct buyer-seller relationship, while it costs a seller to maintain such a connection (

and ). The link costs include, but are not limited to, search cost to locate possible trading

partners, negotiation costs to exchange information and agree on certain business procedures, and

setup costs to integrate two internal information systems.

Bl

Sl 0>Bl

0>Cl

The network formation process is modeled in the following two-stage game:

Stage 1: Buyers and sellers simultaneously determine whether to maintain a link with one

another. They can all observe the consequent network . G

Stage 2: Firms’ private information is revealed (i.e., in the oligopoly market, buyer privately

knows its reservation value ; while in the oligopsony market, seller privately knows its

production cost ); then they compete in the second price auction restricted by the structure of

the network G .

iB

iv jS

jc

There are multiple equilibrium structures under different ranges of connection costs. In this

paper, we focus on least link allocatively-complete (LAC) networks, which are the only efficient

network structure (Kranton and Minehart 2001). Let cl denote the number of products sold when

the market is fully cleared, that is, ) ,( min nmcl = . A buyer-seller network is allocatively

complete (AC) if and only if, for every subset of players from the competing side, there is a cl

- 10 -

feasible allocation in which every player in that subset can complete their transactions. That is,

AC networks can always lead to efficient product allocation under any realization of the private

information at the second stage. In the oligopoly market, the buyers who have the highest

valuation in AC networks can all obtain products from the constrained auction game. Similarly, in

the oligopsony market, only sellers with the lowest production costs can sell their products to

the buyer set if the network is AC. Obviously, when all buyers and all sellers are connected with

each other, the network is AC. Since the connection in the network is costly, an efficient network

should be allocatively complete with a minimal number of links, which is a LAC network.

cl

cl

Definition: A LAC network is a network that guarantees efficient product allocation directly

between a group of buyers and a group of sellers with the fewest overall links.

The structures of LAC networks share several characteristics (Kranton and Minehart 2001). In

the oligopoly market ( ), each seller is linked to exactly nm > 1+− nm buyers, and each buyer

has from 1 to links. Symmetrically, in the oligopsony market ( ), each buyer has just

links, and each seller has from 1 to links. Firms’ positions are heterogeneous on the

competitive side. Figure 1 gives two examples of LAC networks. Please note that the layouts of

LAC networks are not unique.

n mn >

1+−mn m

B1 B2 B3 B4

S1 S2 S3

B5

Figure 1a: A LAC network with 5 buyers and 3 sellers

B1 B2

S1 S2 S3 S4 S5

B3

Figure 1b: A LAC network with 3 buyers and 5 sellers

- 11 -

Proposition 1a and 1b provide the conditions under which the only efficient direct buyer-seller

network, a LAC network, also becomes pairwise stable in the network formation process.

Proposition 1a (Equilibrium of LAC networks in the oligopoly market) ( Kranton and Minehart

2001): For )1(

10 and )1(

10+⎟⎟

⎠

⎞⎜⎜⎝

⎛≤≤

+⎟⎟⎠

⎞⎜⎜⎝

⎛≤≤

mnm

lm

nm

l SB , LAC networks are pairwise stable.

Proposition 1b (Equilibrium of LAC networks in the oligopsony market): For

)1(

10 and )1(

10+⎟⎟

⎠

⎞⎜⎜⎝

⎛≤≤

+⎟⎟⎠

⎞⎜⎜⎝

⎛≤≤

nmn

ln

mn

l SB , LAC networks are pairwise stable3.

From Proposition 1a and 1b, we find how the number of buyers and sellers affects the

endogenous formation of direct buyer-seller networks.

Proposition 2: In direct buyer-seller networks, the more players there are on the competing

side, the less likely that LAC networks will become pairwise stable.

When the number of players on the competing side increases, the difference among them

shrinks. The aggressive competition in the network will reduce the expected marginal gain from

any additional network connection. Consequently, firms have less incentive to keep multiple links,

and it is more difficult for LAC networks to reach equilibrium. In other words, as the competing

side becomes more fragmented, the resulting stable networks are less likely to be efficient.

For LAC networks, we calculate expected payoffs for individual buyers and sellers as well as

social welfare, which refers to the overall payoff of all firms in the network G (Table 2).

Proposition 1 and Table 2 indicate that direct buyer-seller networks have symmetric features in

both the oligopoly and oligopsony markets.

Table 2: Firms’ expected payoffs and expected social welfare in LAC networks (See Appendix

for computation details)

Oligopoly Market Oligopsony Market

3 The proof for Proposition 1a is given by Kranton and Minehart (2001). The proof of Proposition 1b is a symmetric

case of Proposition 1a.

- 12 -

Buyers’

Payoffs

∑∈

+−=

∈

−++

MiB

i

B

BB

nmn

nB

lmm

nn

i

i

i

)1(

and ),...,1( where,buyer

by maintained links ofNumber :)1(2

)1(

iB

λ

λ

λ

λ

)1(1

+−−+− mnl

nmn

B

Seller’s

Payoffs )1(

1+−−

+− nml

mnm

S

∑∈

+−=

∈

−++

NjS

j

S

SS

mnm

mS

lnn

mm

j

j

j

)1(

and ),...,1( where, sell

by maintained links ofNumber :)1(2)1(

jS

λ

λ

λ

λ

Social

Welfare )})(1(

)1(212{ SB llnm

mnmn ++−−++− )})(1(

)1(212{ SB llmn

nmnm ++−−++−

Since the LAC network is the only efficient structure for direct buyer-seller networks, it is

representative of the equilibrium structures before the emergence of the e-market. Direct buyer-

seller networks also have other equilibrium structures under various conditions. The following

analysis can be easily extended to other pre-e-market equilibrium structures and similar insights

can be obtained.

V. The Emergence of a Neutral B2B e-Marketplace

Buyers and sellers each need to maintain multiple connections in order to realize efficient

bilateral exchanges in direct buyer-seller networks. With the entry of a neutral B2B marketplace,

a large number of buyers and sellers can be connected to the other side with a single linkage to

the intermediary (Figure 2). A neutral e-market, such as ChemConnect and PlasticsNet, matches

buyers and sellers and facilitates information exchange, physical deliveries and payments between

them (Bakos 1998). We regard such activities between two firms as linkages and the e-market,

acting as an intermediary, facilitates such relationships and firms’ need to connect to each other.

Buyers and sellers want to build a link with a neutral e-market since they no longer need to

negotiate with each other and adjust their internal IT infrastructures and business processes on a

one-to-one basis.

- 13 -

To be able to facilitate transactions among multiple participants, a neutral e-market has to

invest, I , to build the IT infrastructure and administer the exchange platform. Suppose its profit

comes from the entry fees, and 4Be Se , charged to buyers and sellers, respectively. Buyers and

sellers incur setup costs, and , when they adopt e-market channels. For example, they have

to improve their internal connectivity to meet the requirement of e-marketplaces. If firms join a

neutral e-market, their new connection costs are the sum of the e-market channel setup costs and

the entry fees paid to the e-market. The network transition triggered by the entry of a neutral e-

marketplace can be described as the following two-stage game:

Bs Ss

Stage 1: A neutral e-marketplace enters a direct buyer-seller network. Buyers and sellers

simultaneously determine whether or not to change to an e-market-centered connection by paying

entry fees and incurring e-market channel setup costs. The network G is observable to all

participants.

Stage 2: Firms’ private information is revealed; and they compete in an auction restricted by

the overall linkage pattern.

B1 B2 Bm

S1 S2 Sn

A Neutral e-Market

……

……

Figure 2: A Buyer-Seller Network Centered on a Neutral e-Marketplace

For analytical tractability, we consider only the complete participation scenario, in which a

group of buyers and a group of sellers connect only with each other through a neutral B2B e-

marketplace. Proposition 3 indicates equilibrium conditions under which the efficient direct

buyer-seller network (i.e. a LAC network) is transformed into a neutral B2B e-marketplace.

4 For the unit demand exchange, the entry fee can also be considered as transaction-based. The entry fees could also

be negative, where the intermediary charges fees from one side (the buyer side or the seller side) and subsidizes the

other side to encourage the participation.

- 14 -

Proposition 3a (Equilibrium of a neutral e-market in the oligopoly market): When

, a LAC network will become a neutral e-market that is

pairwise stable as well as efficient.

)(})1{( BBSS slmslnmnI −+−+−≤

Proposition 3b (Equilibrium of a neutral e-market in the oligopsony market): When

, a LAC network will become a neutral e-market that is

pairwise stable as well as efficient. (See Appendix for proof)

)(})1{( SSBB slnslmnmI −+−+−≤

In Table 3, we calculate the expected payoffs for firms and expected social welfare in a neutral

e-marketplace.

Table 3: Firms’ expected payoffs and expected social welfare in a neutral e-market

Oligopoly Market Oligopsony Market

Buyer’s

Payoff BB es

nmn

−−+−

1BB esmm

nn−−

++

)1(2)1(

Seller’s

Payoff SS es

mnm

−−+−

1 SS es

nnmm

−−++

)1(2)1(

A Neutral

e-Market’s

Payoff

Islmslnmn BBSS −−+−+− )(})1{( Islnslmnm SSBB −−+−+− )(})1{(

Social

Welfare Insms

mnmn

SB −−−++−)1(2

)12( Insmsn

mnmSB −−−

++−)1(2

)12(

Through enabling firms to reach a large number of potential trading partners via a single link,

a neutral e-market reduces the total cost to achieve the efficient production allocation among

buyers and sellers. While it alters the overall structure of the buyer-seller exchange network, the

neutral e-market does not change the underlying auction mechanism. Furthermore, the network

migration initiated by neutral e-markets has identical properties in both the oligopoly market and

the oligopsony market, which indicates that market competition has no impact on the emergence

of a neutral e-marketplace. On the contrary, market competition has a profound impact on the

formation of biased e-markets, which will be shown in the next section.

Proposition 4: The lower the e-market channel setup costs incurred by both buyers and sellers,

the easier it will be for a neutral e-marketplace to reach equilibrium.

This is straightforward since firms’ intent to adopt a new interorganizational system is inhibited

by the associated expensive costs. A neutral e-market, with its enhanced technical functions,

- 15 -

simplified operational procedures and a trustful exchange environment, makes the connections

accessible for both buyers and sellers.

Proposition 5: The more buyers and sellers in the network, the easier it will be for a neutral e-

marketplace to reach equilibrium.

From Proposition 3, we find that it is more likely for a neutral e-market to reach equilibrium in

a network with buyers and sellers than in a network with buyers and sellers,

where is any positive integer. Sustainability of a neutral B2B e-marketplace requires high

fragmentation on both the buyer side and the seller side. For example, ChemConnect is a neutral

e-market for chemical trading. Its owner sold one-third of the company to more than 40 chemical

companies to keep these sellers. Meanwhile, these sellers always want to see more buyers online

(Angwin 2004). Many successful neutral B2B e-marketplaces, such as Elance

(http://www.elance.com), have a sufficiently larger number of buyers and sellers.

am + an + m n

a

Proposition 6: The network evolution caused by the entry of a neutral e-market is socially

beneficial. However, the neutral e-market’s incentive to invest is lower than the socially optimal

level.

Proof: In the oligopoly market, a neutral e-market will join the network if, and only if, its

investment cost is lower than . )(})1{(*BBSSInter slmslnmnI −+−+−=

At the same time, in order to increase the social welfare, we need to ensure that:

)})(1()1(212{

)1(2)12(

SBSB llnmm

nmnInsmsm

nmn++−−

++−

≥−−−++− . We denote the investment

level under which the entry of a neutral e-market is socially optimal as:

. Comparing those two equations, we find that

. We will have the same result for the oligopsony market. ■

BBSSSoc mslnmnslnmnI −+−+−+−= )1(})1{(*

0)1)((** ≥−−=− BInterSoc lnnmII

A neutral intermediary gets into a direct buyer-seller network to generate profits and reduce the

overall number of links required for efficient product allocation. Buyers and sellers want to

change to new links only when they can receive better individual payoffs. As a result, social

welfare will increase. However, the positions of firms in prior direct buyer-seller networks are

asymmetric, so some firms have fewer links and save less in connection costs than others. In

order to encourage all firms to join, the neural e-market has to lower entry fees and share part of

the increased social surplus with less-motivated firms. The presence of these less motivated

- 16 -

buyers or sellers, who can benefit from social welfare improvement, causes the difference

between the intermediary’s feasible investment level and the socially optimal investment level.

In this section, we discussed the conditions under which an efficient direct buyer-seller network

will migrate to a neutral B2B e-marketplace. Our analysis revealed factors such as double-sided

fragmentation and low e-market channel setup costs that lead to the equilibrium of a neutral e-

market. We prove that social welfare is improved as the network evolves in this way. In the next

section, we will study the network dynamics triggered by a biased e-market.

VI. The Emergence of a Buyer-Biased B2B e-Marketplace

In addition to neutral e-markets, e-markets can also be created by one side of the market. A

buyer-biased B2B e-marketplace is formed when a group of buyers aggregate their purchasing

power and negotiate lower prices to fulfill transactions with participating sellers. A seller-biased

e-market is the exact mirror case of the buyer-biased e-market, therefore we do not discuss it in

this paper. In a buyer-biased e-market, such as Quadrem and IMX Exchange, buyers can increase

their bargaining power with consolidated demand, and sellers can reach a large number of buyers

with only a single connection. Buyers and sellers incur setup costs, and , when they use e-

market-centered connections. Buyers need to coordinate with each other in order to accomplish

collaborative sourcing, and they can share the e-market setup cost,

Bs Ss

I , with each other.

The next two-stage game illustrates the formation of a buyer-biased e-marketplace.

Stage 1: Buyers decide whether to join a biased e-marketplace by incurring operation costs as

well as e-market channel setup costs. Sellers determine whether or not to connect to the biased e-

market by paying channel setup costs. The network is observable to all participants. G

Stage 2: Firms’ private information is revealed, and they conduct bilateral exchanges restricted

by the overall linkage pattern.

Again, we consider only the complete participation scenario, in which all buyers in the network

join the biased e-marketplace (Figure 3).

- 17 -

B1 B2 Bm

S1 S2 Sn

……A Buyer-biased e-Market

……

Figure 3: A Buyer-Seller Network Centered on a Buyer-biased e-Marketplace

In the oligopoly market, firms’ bargaining power has changed significantly. In the prior direct

buyer-seller network, buyers obtain products at relatively high prices because of competition

among themselves. After all buyers agree to participate in the biased e-market, they gain

monopoly power and are able to appropriate to themselves all sellers’ profits. Buyers can increase

their business benefits from both increased bargaining power and reduced link costs. Researchers

(Jackson 2005) find that the egalitarian allocation rule has very nice properties to align individual

incentives with efficiency. So we apply the egalitarian allocation rule in the consortium, in which

products are delivered to buyers with highest reservation value and the surplus is split equally

among all buyers. In the oligopoly market, the equilibrium condition of a biased e-marketplace is

shown in Proposition 7a.

Proposition 7a (Equilibrium of a buyer-biased e-market in the oligopoly market): When

BSB msnsmlm

nmnI −−++−

<)1()( , a LAC network will evolve to a buyer-biased e-market that is

pairwise stable as well as efficient. (See Appendix for proof)

In the oligopsony market, sellers need to compete with each other in either direct buyer-seller

networks or aggregation networks. The major motivation for buyers to establish the consortium

comes from the reduced number of connections and consolidated business processes with

multiple sellers. After network transition, firms’ bargaining power, as well as the market clearing

price, does not change. We can obtain the evolution equilibrium as follows:

Proposition 7b (Equilibrium of a buyer-biased e-market in the oligopsony market): When

, a LAC network will evolve to a buyer-biased e-market that is pairwise

stable as well as efficient. (See Appendix for proof)

})1{( BB slmnmI −+−<

Again, we list firms’ expected individual payoffs together with expected social welfare of a

buyer-biased e-marketplace in Table 4.

- 18 -

Table 4: Firms’ expected payoffs and expected social welfare in a buyer-biased e-market

Oligopoly Market Oligopsony Market

Buyer’s

Payoff Bs

mI

nmn

−−+−

1mIss

mn

mmnmn

BS −−−++−)1(2

)12(

Seller’s

Payoff

0 Ss

nnmm

−++

)1(2)1(

Social

Welfare Insms

mnmn

SB −−−++−)1(2

)12( Insmsn

mnmSB −−−

++−)1(2

)12(

Based on Proposition 7 and Table 4, we find that the lower the e-market channel setup costs

incurred by buyers and sellers, the easier it will be for a buyer-biased e-marketplace to reach

equilibrium. The reason is the same as in the neutral e-market case.

However, unlike the neutral e-market that behaves similarly in both the oligopoly market and

the oligopsony market, the biased e-market shows different properties when facing different

market competition.

Proposition 8: Sellers’ bargaining power and the market clearing price are reduced more

significantly in the oligopoly market than in the oligopsony market.

In the oligopoly market, buyers compete with each other fiercely before the formation of a

biased e-market. After those buyers aggregate their purchasing power, they can better negotiate

with sellers. In the case of full participation, buyers can even enjoy monopoly power and drive

sellers’ profit to zero. However, in the oligopsony market, it is sellers who compete with each

other in both direct buyer-seller networks and buyer-biased e-markets. The firms’ bargaining

power does not change when the biased e-market is established. It is, thus, more difficult to form

buyer-biased e-markets in the oligopoly market than in the oligopsony market. Sellers in the

oligopoly market are reluctant to join since their bargaining powers are significantly weakened.

Moreover, buyers’ positions are heterogeneous in pre-e-market structures, and it is difficult to

allocate benefits gained from demand aggregation among them (Kaplan and Sawhney 2000). This

confirms our observation that most successful and surviving biased e-markets, such as WWRE,

Quadrem, and Endorsia, are initiated by the side that has less competition prior to forming the e-

markets. It is rare to see sustainable biased e-markets formed by a more competitive side. A

survey of professional buyers (Le et al. 2004) also indicates that most buyers use biased e-

marketplaces for process efficiency rather than interfirm collaboration.

- 19 -

Property 9: The number of sellers has distinctive impacts on the equilibrium of buyer-biased e-

markets in the oligopoly market and the oligopsony market.

In the oligopoly market, it is uncertain how the number of sellers will influence the network

transition. Buyers can save more connection costs if there are more sellers in the network.

However, benefits from increased bargaining power will become less important. By contrast, in

the oligopsony market, a buyer-biased e-market is more likely to reach equilibrium with highly

fragmented sellers because of reduced connection costs and increased seller competition. For

instance, WorldWide Retail Exchange (WWRE) is a successful biased buyer-biased e-market in

the buyer-concentrated retail industry. It connects 59 retailer members and more than 100,000

suppliers.

Proposition 10: In the network migration process caused by a buyer-biased e-market, the

improvement of social welfare in the oligopoly market is uncertain due to involuntary

participation on the seller side. On the contrary, the formation of the buyer-biased e-market will

enhance the social welfare in the oligopsony market.

During the network transition caused by a buyer-biased e-market, buyers want to join the

consortium only if their payoff is better than in pre-e-market structures. In the oligopoly market

after all buyers participate in the consortium, sellers have to switch to e-market-centered

connections even if their payoffs become worse, as they have no choice. The change of social

welfare can go either way depending on the extent of sellers’ total payoff adjustment. In the

oligopsony market, sellers’ bargaining power remains the same and their payoffs increase due to

the reduced connection costs. If not all buyers join buyer-biased markets, buyers cannot fully

capture benefits from enhanced bargaining power, since there is still competition between them.

Sellers’ connection choice becomes much more complicated, depending upon the fraction of

buyers who join the biased market. Future studies are required to explore the incomplete

participation case.

VII. Extension and Generalization

We have made some restrictive specifications in order to make our analysis of the equilibrium

of buyer-seller networks before and after the emergence of B2B e-marketplaces tractable. Next,

we examine our results in a more general setting.

- 20 -

First, we restrict pre-e-market structures to the only efficient direct buyer-seller networks, i.e.,

LAC networks. We can extend our analysis to other pairwise stable structures of direct buyer-

seller networks, in which firms’ pre-e-market payoffs will be different. The equilibrium

conditions of e-marketplaces will change accordingly, but the properties of network transition

processes (Proposition 4, 5, 6, 8, 9, 10) will still hold. When pre-e-market structures are stable but

not efficient, the formation of B2B e-marketplace not only changes network structures, but can

also increase the efficiency of product exchanges. A special type of pre-e-market structure is a

null network with previously unconnected buyers and sellers, when direct buyer-seller links are

prohibitively expensive due to causes such as geographical dispersion. In this case, firms’ pre-e-

market payoffs are zero, and B2B e-marketplaces are more likely to emerge.

In our model, we only discuss the complete participation cases. If there are both direct buyer-

seller connections and e-market links, it is more challenging for B2B e-markets to succeed. With

the existence of direct buyer-seller links, not all firms in the network will join the e-market in

equilibrium. A neutral e-market’s payoff will shrink with fewer participating buyers and sellers.

A biased e-market’s bargaining power cannot increase as much as in the complete participation

scenario in the oligopoly market, and the number of participating sellers decreases in the

oligopsony market. We can apply the same argument to the case where competing e-markets

operate in one buyer-seller network.

Finally, our model is a one-shot game and represents spot sourcing for commodity rather than

systematic sourcing. In a spot market, firms establish arm’s length relationships to explore trading

opportunities and conduct transactions, just as we have analyzed in the model. However, for

systematic sourcing, long-term relationships are important. We do not discuss aspects of long-

term B2B relationships, such as information sharing, or coordination and trust, in our paper. Grey

et al. (2005) provide a survey of the opportunities and difficulties a B2B e-market faces by

preserving and complementing existing long-term buyer-seller relationships.

VIII. Concluding Remarks

In this paper, we study the dynamics of buyer-seller networks initiated by B2B e-marketplaces

through a multiple-person two-stage game. By examining the network equilibrium conditions, we

identify several factors leading to sustainable B2B e-marketplaces.

- 21 -

The first critical factor is low e-market channel setup costs. This is straightforward in that firms

are only willing to join an e-market when the process to establish an e-market channel is simple

and painless. Consequently, e-Marketplaces, both neutral and biased ones, are more likely to

emerge and succeed after Internet infrastructure and access become prevalent, reliable and

inexpensive. For instance, the usage of airline industry e-markets in Asia was higher in developed

countries, such as Singapore, than in developing countries, such as China. The reason is that

developed countries have more mature Internet infrastructures (Neill and Purchase 2004).

The second critical factor is the number of buyers and sellers. A neutral e-market is more likely

to survive with more buyers and sellers in the network. For a biased e-market, the number of

firms on the non-owner side has different effects depending on market competition. In a buyer-

biased case, e-marketplaces in the oligopsony market are more likely to sustain with a more

fragmented seller side. However, in the oligopoly market, the effect of the number of sellers on

the e-market equilibrium is uncertain.

Third, the sustainability of a neutral e-market has an equal chance in both the oligopoly market

and oligopsony markets. However, a biased e-market is less likely to succeed if it is formed by

the more competitive side because the owner side’s bargaining power will increase significantly,

and the other side will act strongly against the formation of such e-markets.

We also study the social welfare implications of B2B e-marketplaces. Social welfare is

improved with the formation of a neutral e-market, although a neutral e-market’s investment

incentive is lower than the socially optimal level. However, when a biased e-market emerges, it is

uncertain how social welfare will change due to involuntary participation on the non-owner side.

We believe our work has made several theoretical contributions to B2B e-marketplace studies.

We provide a network level analysis of B2B e-marketplaces, in which a firm’s performance is

constrained by the overall network structure and the relative positions of players within it. We are

able to recognize several key successful factors of B2B e-marketplaces. Our analysis suggests that

ownership structures, market competition, and previous buyer-seller relationships jointly affect

the sustainability of B2B e-marketplaces. We highlight the importance of adopting a network

dynamics perspective to study digital B2B networks, since new inter-firm connections keep

emerging and firms can use them to substitute for old ones.

B2B e-marketplaces are still evolving (Gosain and Palmer 2004; Le, et al. 2004). While we

identify several necessary conditions for successful B2B e-marketplaces, these conditions are

- 22 -

unlikely to become jointly sufficient. Further studies, including empirical ones, are needed to

explore the indicators of B2B e-marketplaces performance (Laseter and Bodily 2004). Future

studies can develop similar network economics models to study the dynamics and economic

impacts of other types of digital B2B networks, including private e-marketplaces formed by

industry leaders such as Wal-Mart and Cisco.

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Appendix

Table 2: Calculation of firms’ expected individual payoffs and expected social welfare.

Proof: We will only provide computation for the oligopoly market case. Readers can get the

results for the oligopsony market case by following the same approach.

We use mhY : to denote the highest reservation value among buyers. In LAC networks, the

expected market clearing price will be

thh

1)( :1

+−

=+

mnmYE mn , which is determined by the second

price auction. Since each seller has 1+− nm links in LAC networks,

)1(1

)]([ +−−+−

= nmlm

nmGE SSLAC jπ .

The number of buyers’ connections ranges from 1 to . For buyer with n iBiBλ links,

- 25 -

i

i

i

i

BB

BB

BBmnmm

BLAC

lmm

nn

lmm

nm

nm

lm

nmYEm

nmYEm

nmYEm

GE

λ

λ

λ

π

−++

=

−+

+++−

++

=

−+−

−+++−

−++−

−=

)1(2)1(

)1

1...11

1(1

]}1

)([...]1

)([]1

)({[1

)]([

::2:1

.

Social welfare is the sum of players’ individual payoffs in the network. In the paper, we use W

to indicate social welfare. The expected social welfare in the LAC network is:

)}1)(()1(212{)]([)]([*)( +−+−

++−

=+= ∑∈

nmllm

nmnGEGEnWE SBMi

BLACSLACLAC ijππ . ■

Proposition 3a (Equilibrium of a neutral e-market in the oligopoly market): When

, a LAC network will evolve to a neutral e-market that is

stable as well as efficient.

)(})1{( BBSS slmslnmnI −+−+−<

Proof: Similar to LAC networks, a neutral e-market with complete participation also facilitates

efficient good allocation. Therefore, the market clearing price will be the same in two situations.

In order to motivate all buyers and sellers to participate, a neutral B2B marketplace owner should

charge the entry fees where:

Ineme SB −+ max

.. BBB lsets ≤+

SSS lnmse )1( +−≤+

Therefore, , and BBB sle −= SSS slnme −+−= )1( .

A neutral e-market owner is willing to invest when 0≥−+ Ineme SB , that is

, and all buyers and sellers are willing to join. Please note

that we only consider the lower boundary case in the proof. The intermediary usually charges flat

fees for buyers or sellers. The number of buyers’ links in LAC networks ranges from 1 to . If

the buyer with only one link in LAC networks has the incentive to join, all other buyers will

choose to switch to e-market-centered connections too. For the oligopsony market case, the proof

is the same. ■

)(})1{( BBSS slmslnmnI −+−+−≤

n

- 26 -

Proposition 7a (Equilibrium of a buyer-biased e-market in the oligopoly market): When

BSB msnsmlm

nmnI −−++−

<)1()( , LAC networks will evolve to a buyer-biased e-market that is

pairwise stable as well as efficient.

Proof: When all buyers join the consortium, they can set the price as low as to achieve

efficient product allocation. Sellers have to connect to the biased e-market to facilitate future

transactions even when their expected payoff becomes 0. Buyers’ total surplus is:

Ss

BS

BSmnmm

mskmnsm

nmnmskmnsYEYEYE

−−−++−

=

−−−+++

2

2::2:1

)1(2)12(

)(...)()(

Then each buyer’s expected payoff is: BS smIs

mn

mmnmn

−−−++−)1(2

)12( . In order to convince all

buyers to participate the consortium, we need to have:

BBS lmm

nnsmIs

mn

mmnmn

−++

>−−−++−

)1(2)1(

)1(2)12( .

From which we can obtain the equilibrium condition: BSB msnsmlm

nmnI −−++−

<)1()( . ■

Proposition 7b (Equilibrium of a buyer-biased e-market in the oligopsony market): When

})1{(1BB slmn

mk −+−< , a LAC network will evolve to a buyer-biased e-market that is

pairwise stable as well as efficient.

Proof: To achieve efficient product allocation, the market clearing price is still determined by

the second price auction due to incomplete information of sellers’ production cost. Therefore, the

expected market price will be 11

1)(1)( :

++

=+

−−+=−

nm

nmnnXE nmn , the same in a LAC network.

If buyers are willing to form the consortium, it should be: )1( +−<+ mnlsmI

BB . ■

- 27 -