Customer Retention in a Product Platform World

Gil Appel

Michael Haenlein

Barak Libai

Eitan Muller

December 2017

Gil Appel is Assistant Professor of Marketing, Marshall School of Business, University of Southern California, Los Angeles, 90007, gappel@marshall.usc.edu

Michael Haenlein is Professor in the Marketing Group at ESCP Europe, 79 Avenue de la République, F-75011 Paris, France, haenlein@escpeurope.eu

Barak Libai is Professor in the Marketing Group at the Arison School of Business, Interdisciplinary Center, Herzliya, Israel, libai@idc.ac.il.

Eitan Muller is Research Professor of Marketing, Stern School of Business, New York University, New York, NY, 10012; and Professor of Marketing, Arison School of Business, Interdisciplinary Center, Herzliya, Israel, emuller@stern.nyu.edu

The authors wish to thank the seminar participants at HEC Paris and the University of Maryland for their helpful comments.

Abstract

In mobile digital environments, we observe increasing use of cross-promotion activities in which firms proactively churn their customers toward other products. This practice may appear to challenge the conventional wisdom of the importance of customer retention, in particular of high-value customers. Yet past work in this area has largely focused on the case of a single product, while firms are increasingly advised to manage their offerings as “product platforms” that consist of families of products with a common underlying logic. Taking a product platform view, when a new product enters the market, users of current products may be good candidates for acquisition efforts toward the new offering. Applying a customer lifetime value (CLV) approach and using the digital gaming industry as an example, we show that when customer engagement declines over time, it should be in the firm’s interest to use cross promotion to churn even its best customers from current products and transfer them to a newer product. We examine the factors that affect the profitability of moving from a single product lifetime value to product platform lifetime value; consider the possible impact of other factors such as social influence on other customers; demonstrate sensitivity analysis of customer transferal for the case of a mobile gaming company; and discuss the implications for the results on the management of customers in the contemporary market environment.

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One of the most interesting developments in the digital space in recent years is the rise of

cross promotion as a strategic tool for the transfer of customers among products. Cross

promotion, which occurs when customers of one product are targeted with a promotion for a

related product, is not a new phenomenon: It has long been known that brands can take

advantage of other brands to access potential customers or to reach new markets in a cost-

efficient manner (Gruner 1997; Thota and Biswas 2009). Yet in recent years, cross promotion

has become more than just one among many tools in the marketing mix, as a rising number of

markets have been transformed into “product platforms” comprised of interconnected products

(Sviokla and Paoni 2005). In such markets, various products affect each other’s acquisition and

retention to maximize overall customer equity, consistent with the logic underlying cross

promotion.

While the emergence of product platforms is most prominent in the digital sphere, the

underlying phenomenon has wide-ranging implications for market management in general. In

what follows, we use the term “product platform” in a broad sense, not limited to two-sided

markets as it has occasionally been applied in prior literature (Landsman and Stremersch 2011).

Our aim is to explore the customer management implications of this phenomenon. We hereby

specifically focus on how and when cross promotion should take place; and how industry views

on customer retention and customer lifetime value should be updated to the reality of customer

transferal in product platforms.

We illustrate our approach in the context of the digital gaming industry, in particular

mobile gaming. The gaming industry is notable for its scope and fundamental effects on digital

markets. Its worth is projected to reach $110 billion in 2017 (with mobile games representing

42% of that figure), far higher than industries such as motion pictures and music (McDonald

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2017). In 2017, 65% of U.S. households were home to at least one member who played three or

more hours of video games a week, attracting both genders (women representing 31%) with an

average player age of 35 (Entertainment Software Association 2017).

A notable characteristic of the (mobile) gaming industry is a sharp decline in engagement

over time, resulting from the natural exhaustion that occurs after playing a game for a certain

duration. An illustration of this can be found when looking at the time spent with a game per day,

which tends to decrease dramatically within the first two weeks of playing (Adjust.com 2016).

This declining engagement results in an environment comparable to the one encountered by

many FMCG manufacturers, where consumers are affected by variety seeking and are constantly

driven to try new products (Kahn 1995). Much work has examined optimal firm behavior in such

markets, and focused on questions of pricing, positioning, and promotions (Kim 2013; Sajeesh

and Raju 2010; Seetharaman and Che 2009).

Given these similarities, game publishers apply similar strategies to those of FMCG

companies to address the issue. A near-ubiquitous approach in this context is to release an

increasing number of games into the market (many of which are short term in nature) to capture

customers’ engagement early on (Perez 2016). In May 2016, for example, the games category

alone accounted for 43% of new apps in the Apple Store, with the next category (education)

accounting for about 5% (Nelson 2016). In addition, the ability to follow and manage customers

allows the industry to bring individual customer management approaches to markets

characterized by variety seeking. As firms are increasingly able to conduct customer

management in markets that were historically product based only (Kumar and Shah 2015), we

believe our insights from the gaming industry will become even more relevant to various variety-

seeking markets beyond gaming in the near future.

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To manage the platform of games that results from such sequential releases, firms apply

two different kinds of cross-promotion strategies. The first one is external cross promotion, in

which game publishers encourage customers to move to a game of a different brand, in exchange

for acquiring new customers from other publishers at the same time. The second strategy, and

our focus herein, is internal cross promotion, where publishers create a portfolio of games that

push each other’s growth via cross promotion within the brand (Chupa Team 2015; Vaghari

2017). Internal cross promotion is commonly applied by larger firms in the mobile gaming

industry, such as Disney (Wong 2016) and Ketchapp (Chupa Team 2015).

An intriguing aspect of internal cross promotion is that it requires taking a fresh look at

customer retention. The idea that a firm may want to actively churn a product’s profitable

customers from one product to another appears to turn the conventional wisdom of customer

management on its head. For more than two decades, marketers’ attention has been drawn to the

importance of customer retention and the need to achieve “zero defections” (Reichheld and

Sasser 1990). While it is generally accepted that the firm may not want to retain some less

profitable customers (Haenlein and Kaplan 2009; Haenlein, Kaplan, and Schoder 2006; Shin,

Sudhir, and Yoon 2012), the importance of customer retention has been cited consistently and

extensively. In that vein, research has demonstrated its effect on the bottom line, developed

methods to reduce churn, and considered the tradeoff of investment between retention and

acquisition (Ascarza et al. 2017).

A shortcoming in this approach, however, is that it largely reflects a single-product view,

and that recent efforts have focused more on a product-level analysis and less on the

management of individual customers and their profitability across products. Moving from a

single-product mindset to a product platform view can have game-changing effects on basic

4

principles of customer management. In a platform world, the best potential customers of a new

product might be current users of an existing product. Firms may therefore want to proactively

churn a given product’s customers by encouraging them to transfer their engagement to another

product. In fact, we will show that it may actually be the product’s best customers that the firm

would want to churn. Insights on acquisition and retention that were formed in a single-product

context therefore need to be fundamentally reexamined in a world when one product’s churn is

another product’s acquisition.

Our aim is to understand under which conditions cross promotion is profitable, and which

factors affect this profitability. To do so, we rely on a customer lifetime value (CLV) analysis

that has become the cornerstone of customer management thinking in recent years (Gupta et al.

2006; Kumar and Shah 2015). In this framework, we examine how the CLV of a customer

changes if the firm moves from a single-product environment to a product platform environment.

Our results show that in a world where customer engagement is declining over time, the CLV of

a customer within a platform is higher than the CLV of a single product, which helps to explain

the fundamental motivation for cross promotion. In addition, we show that the firm’s incentive to

conduct cross promotion increases when customers’ organic tendencies to move to the next

product is stronger; when customers’ tendency to churn the platform is stronger; and when

customer per-period profitability is higher.

What these results imply is that it can be in the firm’s interest to churn a product’s best

customers in order to move them to the next product, which intuitively contradicts basic CRM

thinking (Haenlein 2017). We demonstrate the scope of these effects in an empirical dataset of a

platform containing four gaming apps. Our results also shed light on the motivation for external

cross promotion, where customers come and go between brands. We further show how the social

5

influence aspects of cross promotion – which are not explicitly captured in the CLV framework

we apply – only strengthen the motivation for cross promotion that we identify here.

Related Literature

Our study is related to and draws from three different research streams: work on product

platforms, customer retention, and cross-selling. We now discuss each of these research streams

and its relationship to cross promotion in more detail.

Product Platforms

The term “platform” has been used in various ways in prior research, including but not

limited to organizational platforms, market intermediary platforms, platform ecosystems, and

product family platforms (Thomas, Autio, and Gann 2014). Our work is focused on the latter –

product family platforms – by looking at firm decisions in the context of a portfolio of substitute

products. While studies in the strategy and new product domains have analyzed platforms from

the perspective of design commonalities and resource allocation among products (Klingebiel and

Rammer 2014), we focus on the inter-product effect on customer management.

By taking a multi-product view, our work addresses marketing efforts such as the

analysis of how complementary products and categories affect other products’ adoption

decisions (Sriram, Chintagunta, and Agarwal 2010); how movie sequels create profitability

(Dhar, Sun, and Weinberg 2012); and how products’ values are affected by how they receive and

send customers to each other (Oestreicher-Singer et al. 2013). We diverge from these efforts by

taking an individual customer view, and by focusing on CLV rather than product profitability as

the main dependent variable.

6

Platform issues also arise in the diffusion of innovation literature, specifically studies

aimed at understanding how technological generations substitute each other (Norton and Bass

1987). These studies have been devoted to understanding whether the pace of growth changes

between generations (Peres, Muller, and Mahajan 2010), as well as decisions on optimal pricing

(Danaher, Hardie, and Putsis 2001) or optimal introduction time (Mahajan and Muller 1996). In

contrast to our approach, this avenue of research has relied on aggregate product diffusion type

approaches, and did not expand upon individual customer profitability issues.

Customer Retention

Classic CRM thinking by both practitioners and academics has cited the importance of

customer retention for profitability and the need to prevent and predict customer churn (Ascarza,

Iyengar, and Schleicher 2016; Ascarza et al. 2017; Gupta, Lehmann, and Stuart 2004; Reichheld

and Sasser 1990). Consistent with these findings, our work does not question the need to retain

customers. Instead, we argue that retention needs to be analyzed in a larger context, not focused

on the single product, but rather on the platform as a whole.

This shift in perspective has implications for various aspects of customer management.

For example, when looking at the tradeoff between customer acquisition and customer retention,

prior research examined issues such as the differing cost structure of acquisition and retention

activities (Min et al. 2016), the scope of responsiveness to CRM efforts (Musalem and Joshi

2009), or the relationship between time to acquisition and retention (Schweidel, Fader, and

Bradlow 2008). Moving from a single product to a platform view naturally extends our

understanding of these tradeoffs. It also has implications for the measurement of CLV, where

retention plays a fundamental role (Kumar and Pansari 2015; Kumar et al. 2008), as prior

research in this area has generally been conducted by using a single product as the unit of

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analysis (Gupta et al. 2006). We extend CLV research by explicitly modeling the tradeoffs

involved in multi-product management.

Cross selling

In its essence, the decision to transfer a customer from one product to another can be

considered cross-selling. Work in this area has focused on issues such as identifying the best

next product to offer, which customers are more tractable to cross selling, or the optimal timing

and use of communication channels (Knott, Hayes, and Neslin 2002; Li, Sun, and Montgomery

2011; Prins and Verhoef 2007; Schmitz, Lee, and Lilien 2014). While it has generally been

accepted that cross selling results in an increase in CLV (Kumar, George, and Pancras 2008), it

has been argued that cross selling to unprofitable customers can have negative effects on

profitability (Shah et al. 2012). We add to this literature the need to analyze the tradeoff created

in product platforms where cross selling can result in loss of CLV in the current products while

increasing overall customer equity.

How Cross Promotion Impacts CLV in a Product Platform

Types of Cross Promotion

Before we present our analysis, it is important to clarify the typology of cross promotion

activities. Interviews we conducted with managers in the gaming industry, as well as a review of

the related business literature, suggest the appropriateness of a 2x2 matrix to characterize the

cross-promotion business scenario (see Table 1).

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Table 1: Types of Cross-Promotion Strategies

Create Direct Engagement (Customer Lifetime Value)

Create Indirect Engagement (Customer Social Value)

Internal Cross Promotion Direct – Internal(our focus)

Indirect – Internal

External Cross Promotion Direct – External Indirect – External

Beyond the two basic type of cross promotion (i.e., internal and external), consider the

motivation for cross promotion, specifically the creation of direct or indirect engagement. Direct

engagement aims at enhancing the CLV of customers who are being transferred, or acquiring

other customers with higher CLVs. Indirect engagement takes into account the fact that

customers can affect the CLV of other customers via social influence, and aims to use cross

promotion to maximize this social influence. An example of an indirect engagement motivation

can be found in the mobile gaming industry, where rankings in popularity charts have a strong

effect on demand. The transferal of a sufficient number of customers to a game early on in its life

cycle can improve ranking positions favorably, and in turn have a strong influence on the ability

to acquire other customers (Chupa Team 2015). While our focus is mostly on the direct –

internal case (“northeast” quadrant, Table 1), we will later discuss our results in the context of

the other quadrants as well. In managerial practice, firms may combine multiple motivations and

types in employing cross promotion.

The context: A two-product platform

Our objective is to compare the CLV of a customer consuming a single product (Product 1)

with the CLV of a customer in a platform who is cross promoted from one product to another

(from Product 1 to Product 2). While we use the market for mobile digital games as a context,

our analysis is relevant to platforms in general. Therefore, we use the words “product” and

9

“game” interchangeably. For expositional simplicity, we focus on the case of two successive and

similar products. As we will discuss later, the fundamental insights from such a two-product

scenario extend to larger, multi-product platforms.

One point that requires clarification is the concept of “similarity” between products: Our

analysis considers two products to be similar if they are comparable in their drivers of

profitability (i.e., gross profit per period and retention). We do not require similarity in specific

product characteristics (e.g., game features). It is therefore immediately intuitive that cross

promotion can create profit if products are non-similar (e.g., if one product generates a higher

CLV than the other). Yet our analysis shows that even when products are similar in terms of their

profitability drivers, firms may still have a motivation to transfer customers.

A Platform Benefit Model

We use a fundamental approach to CLV modeling, where the CLV of an individual can

be represented as

(1) CLV=∑t=0

T r t ∙ P(1+d)t+1 ,

which in the case of infinite horizon, sums to

(2) CLV =CLV ∞=P

1+d−r .

Whereby r is the individual-level retention probability per period t; P is a fixed gross

profit per period; and d is the discount rate (Kumar and Pansari 2015; Kumar, Ramani, and

Bohling 2004). We consider a two-product platform in which Product 1 is introduced at Period 1

and continues after the introduction of Product 2 that occurs at Period T+1. Thus, before Period

T, only one product is available that belongs to the platform, while from Period T+1 onwards,

two products are available (see Figure 1).

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Figure 1: Product Platform with two Games

0 1 2 … T T+1 …

Game 1

Game 2

We assume that between t = 1 and t = T, customers of Product 1 can churn only externally

(out of the platform), while from period t = T+1 onwards, customers of Product 1 can churn

externally (out of the platform) and internally (to Product 2). Customers of Product 2 can churn

externally only, as we do not include a third product in the platform. That being said, it is

straightforward to construct a multi-product platform along the same lines mutatis mutandis –

see our empirical illustration below. In this setting, we need to distinguish two types of

individual-level retention probabilities:

ro is the probability of remaining in the platform (outside retention). Thus 1−ro is the probability of churning externally (out of the platform). We assume that both churn and revenue realization occur at the end of each period. This assumption can easily be changed and results in a straightforward modification of our results.

ri is the probability of remaining with Product 1 and not moving to Product 2, given that the consumer has not exited the platform (internal retention). Therefore 1−r i is the probability of churning internally or transferring from Product 1 to Product 2. We assume customer transferal occurs at the beginning of the period.

Looking at ri, note that internal retention is influenced not only by the firm’s cross-

promotion activities, as customers can also organically move among products without firm

intervention. Cross promotion aims to reduce any organic internal retention by actively

11

transferring customers to another product. The question we focus on is whether and when a firm

should actively conduct such activities.

We assume that consumers can consume only one product at any given time and do not

consume both products simultaneously. It is obvious that in a case where the consumption of

Product 2 simply adds to that of Product 1, cross promotion is beneficial. This is, however, not a

realistic assumption, as many products compete for users’ time. In the mobile world, for

example, consumers may download a large number of apps but in fact only use a small subset of

them (Luckerson 2015). In addition, consumers usually do not play much more than one game

per day (Hwong 2016). Thus, even if they may have a short period of simultaneous playing, we

assume that successful cross promotion results in churn from the first one.

The case of constant gross profit per period

Given these assumptions, Table 2 shows the value created by a consumer who adopts

Product 1 at Period 1, and then retains Product 1 after Period T+1 with probability ri(per period).

Note that up to Period T, the value created precisely follows a conventional CLV creation, while

beginning at Period T+1, the consumer has two retention probabilities:ro (the probability of

staying within the platform), and ri (the probability of staying within the product and not

transferring from Product1 to Product 2).

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Table 2: Value Created by a Consumer of Product 1 (Constant Per-Period Profit)

Period 1 2 3 T

Product 1 P 11+d P

ro

(1+d )2P

r o2

(1+d )3P

roT −1

(1+d )T

Period T + 1 T + 2 T + k

Product 1P ri

roT

(1+d )T +1 P ri2 ro

T +1

(1+d )T +2 P r ik ro

T +k−1

(1+d )T +k

Product 2P (1−r i )

r oT

(1+d )T +1 P(1−r i2)

r oT +1

(1+d )T +2 P(1−r ik)

roT + k−1

(1+d )T +k

Product 1 +

Product 2P

roT

(1+d )T +1 Pr o

T+1

(1+d )T +2 Pro

T +k−1

(1+d )T +k

Observe Period T+2 in Table 2 for an illustration. The probability that the customer is still

active at T+2 (i.e., has not yet left the platform) is roT +1. During T+2, the customer can either be a

user of Product 1, which implies that she remained with Product 1 for two periods (T+1 and

T+2), an event that occurs with probability ri2. Or, the customer can be a user of Product 2. This

can happen either because she already adopted Product 2 in Period T+1 with probability 1−r i, or

because she adopted Product 2 in Period T+1 with probability ri(1−r i). The total probability of

being a user of Product 2 is then 1−ri+ri (1−r i )=1−r i2. In both cases, the gross profit per period

generated in T+2 is P, which needs to be discounted accordingly.

The last row of Table 2 sums the value created in the platform by both products. The exact

set of transferal and retention events from one product to the next is detailed in Appendix A.

Given that the gross profit per period is constant over time and identical for both products, it is

easy to show that summing up the value created by both products from Period 1 to infinity

results in the standard CLV of formula (Equation 2) with retention rate ro. Specifically, the total

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value does not depend upon the internal retention ri. For two similar products with constant and

identical gross profit per period, cross promotion that will result in customer transferal does not

create additional value.

The Case of Changing Gross Profit per Period

The aforementioned picture becomes more complex when customer profitability changes

over time. To better understand how such a change affects overall platform profitability, we first

need to look at the two factors that drive CLV – retention probability and per period profitability

– and how these factors may change over time.

To answer the question of a change in individual retention probability over time, it is

necessary to carefully distinguish between cohort and individual-level change. At the cohort

level, average retention rates will increase over time even if at the individual level, customer

retention remains stable. This is due to heterogeneity among customers in their retention rates

under which lower-retention customers leave early (Fader and Hardie 2010), pushing up the

average retention rate at the cohort level among the remaining customers. Consequently, a

potential increase in retention rates at the cohort level cannot be seen as an indication that

individual-level retention probabilities change over time.

Looking at per-period profitability, popular work done by Bain suggests that per-period

profit tends to increase over time (Reichheld and Sasser 1990; Reichheld and Schefter 2000). Yet

these generalizations have been challenged (Dowling 2002; Reinartz and Kumar 2000). Overall,

it has been argued that a change in customer profitability over time – be it an increase or a

decrease – may depend on the customer’s attitude toward the specific brand and her preference

for a relationship with it (Johnson, Herrmann, and Huber 2006; Umashankar, Bhagwat, and

Kumar 2017; Verhoef 2003). Individual per-period profitability may therefore differ

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considerably among customer segments (Mark et al. 2013) and the answer is likely to be market

specific. As discussed above, a notable characteristic of the (mobile) gaming industry is a sharp

decline in engagement over time. In what follows, we therefore assume a declining expected

profit pattern in the form of δ t, where t is the period, and δ ≤ 1.

A potential decline in per-period profitability can be caused by two distinct processes:

product-related decline, which begins with the product’s introduction; and consumer-related

decline, which begins with the consumer’s adoption. The processes underlying these two types

of decline differ. Product-related decline might occur due to the product losing its appeal as it

ages. It occurs when the current and potential customers are looking for exciting new products,

and thus spend more time with new products than with old ones, regardless of the individual

customer’s time of adoption. On the other hand, consumer-related decline might occur due to

diminishing engagement of the individual customer with the product, regardless of competing

products.

In Appendix A, we formalize those two approaches, while here we discuss briefly their

implications. In the case of product-related decline, Product 2 begins with per-period profit of P

in Period T+1. In later periods, per-period profit declines at a rate of 1−δ per period. Thus, if a

given customer adopts in Period T + k, the per-period profit generated from this customer in this

period is P δ k−1, even though Period T + k represents her first period of using the product. In

consumer-related decline, per-period profit generated from the same customer at this period is P,

as decline only kicks in once the product has actually been adopted.

In the following sections, we focus on product-related decline due to its relative simplicity.

However, it can be shown that the CLV of a consumer under consumer-related decline is always

higher than the corresponding CLV under product-related decline (see Proposition A in

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Appendix A). We therefore expect our results to be stronger in the case of consumer-related

decline. In reality, we should observe both declines, possibly at differing rates.

Table 3 mirrors Table 2 for the case of changing per-period profits with product-related

decline. Product 2 begins with a per-period profit of P in Period T+1, and then profit declines at

a rate of 1−δ per period. Note that our argument so far assumes decreasing per-period

profitability, yet the parameter δ can also capture a potential decline in retention. One could even

argue that any drop in engagement over time will be correlated with an associated decreasing

retention probability, yet evidence on this is not available. In addition, decreasing engagement

may be correlated with lower social influence on others. While we do not formally model this,

further on we discuss how this should also be consistent with our results.

Table 3: Value Created by a Consumer of Product 1 (Declining Per-Period Profit)

Period 1 2 3 T

Product 1 P 11+d Pδ

ro

(1+d )2P δ2 r o

2

(1+d )3P δT −1 r o

T−1

(1+d )T

Period T + 1 T + 2 T + k

Product 1P δT r i

r oT

(1+d )T +1 P δT +1 ri2 ro

T +1

(1+d )T +2 P δT + k−1 r ik ro

T +k−1

(1+d )T +k

Product 2P (1−r i )

r oT

(1+d )T +1 Pδ (1−ri2)

r oT +1

(1+d )T +2 P δ k−1(1−rik )

r oT +k−1

(1+d )T +k

Based on the pattern of value creation depicted in Table 3, it is possible to derive an

expression for the CLV of a customer within the platform. This CLV has three components: the

value from the consumption of Product 1 between Periods 1 and T; the value from the

consumption of Product 1 between T+1 and infinity; and the value from the consumption of

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Product 2 between T+1 and infinity. The formal derivation is described in Appendix B and leads

to the following result reflecting the platform benefit:

(3) Platform Benefit ¿ P( ro

1+d )T

(1−δT )( 11+d−δ ro

−r i

1+d−δ ro ri)

It is obvious from Equation (1), that when per-period profit is flat (δ=1 ), or when there is

no consumer transfer between Product 1 and Product 2 (ri=1 ), the platform benefit is zero – with

the exception of the trivial cases P=0 and ro=0. We also see that no terms in Equation (3) can

be negative, with the exception of 1−δT . Therefore the platform benefit is indeed positive if and

only if 1−δT>0, or δ <1. If engagement increases over time, there is no benefit for customer

transferal among similar products.

When should firms cross promote to transfer their customers?

As aforementioned, the internal retention rate r iin Equation (3) is influenced by a

customer’s organic propensity to move among products, and by any firm cross-promotion

activities (as ri represents internal retention, cross-promotion is 1−r i). Under which conditions

does the firm have an incentive to further cross promote under declining per-period profit? To

examine this question, we look at the effect of change in 1−r ion platform benefit, which is the

partial derivative of the platform benefit with respect to 1−ri. It is straightforward to verify

(Appendix C – Part 1) that under declining engagement (δ ≤ 1), this partial derivative is always

positive. Thus, if the firm increases cross promotion, platform benefit will increase, which leads

to the following proposition:

Proposition 1: The firm benefits from cross promotion if engagement declines over time. Conversely, the firm loses from cross promotion if engagement increases.

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Knowing that customer transferal may be beneficial, the question becomes which factors

affect this profitability, that is, how the rate of change in the impact of cross promotion on

platform benefit is affected by the parameters of the model. Answering this requires taking the

derivative of the platform benefits with respect to 1−ri(the rate of cross promotion) and

differentiating this term with respect to other characteristics of the platform. This analysis is

presented in Appendix C. Next, we discuss the results for the various aspects of the platform

characteristics.

Internal retention: When would cross promotion be more beneficial? When customers

tend to move among products on their own (low r i), or when they tend to stay with the current

product and are less prone to move to new ones (high ri)? The second derivative of platform

benefit with respect to cross promotion and r i shows that cross promotion is more beneficial

when the organic level of r iis higher (Appendix C – Part 2). To see that note that the lower the

organic retention (i.e., the higher the tendency customers will move among products on their

own) the higher the platform benefit (Appendix C – Part 1). The question is where the firm’s

efforts to cross promote would be most effective, given that. We see that when internal retention

is higher (i.e., platform benefit is lower) cross promotion will have the most impact as the

marginal effect in this situation is particularly high.

Outside retention: The level of outside retention may be a function of a specific product,

but also of the category as a whole. Industry reports suggest that there are a notable differences

among product categories in their respective tendencies to churn (Klotzbach 2016). At a first

glance, one could assume that a higher tendency to leave the platform should lead to a higher

benefit of cross promotion, since it may be better to transfer a customer to the next product

before she leaves altogether. However, note that in the case of similar products, the tendency to

18

leave the platform will transfer to the second product as well, so the transferal does not change

the situation per se. Indeed, our analysis (Appendix C – Part 3) shows the opposite to be true:

The higher the external retention rate, the more incentive the firm has to transfer customers

through cross promotion. Since in Product 2 engagement starts higher, more benefit is created.

Thus, the higher the external retention rate, the higher the probability that this benefit will

continue.

Gross per-period profit: In our model, the parameter P represents the initial level of

customer profitability (which declines over time). If P is higher, the customer is more profitable

for the firm. Intuitively, we expect a higher level of P to increase the benefit of moving a

customer, as any difference in profit due to differential engagement will increase. Indeed, this is

what we see in our derivations (Appendix C – Part 4).

The above is summarized in the following proposition:

Proposition 2. The incentive of the firm to conduct cross promotion is increasing when (a) the organic tendency of customers to move to the next product is weaker; (b) customers’ tendencies to churn the platform are lower; and (c) per-period customer profitability is higher

Note that Proposition 2 does not include a sub-proposition expressing the potential

impact of engagement decline . The reason is that the relationship of cross-promotion benefit to

engagement decline is non-linear (Appendix C – Part 5). This may seem surprising, as

engagement decline is needed to create the platform benefit, so that one may expect a sharper

decline be to be associated with high cross-promotion benefit, as the difference between the two

products is larger. Yet a sharper engagement decline also reduces the CLV of the customers in

the second product post move. These competing effects create an inverted-U-shaped curve on the

relationship (see Appendix C – Part 5).

19

Data-Based Sensitivity Analysis

We augment our argument by providing an empirical illustration in which we estimate the

sensitivity of the platform benefit to changes in cross promotion in a real-world setting. The

measure of interest in this case is the percentage of improvement in the platform’s benefit if

cross promotion is increased by 1%.

To calibrate the relevant parameters, we obtained a dataset from an established publisher of

multiple mobile game apps, several of which reached the Top 100 in the major app stores in

recent years. Our dataset consists of data on the adoption and retention of four consecutive apps.

The lifetime of each app is typically less than three months, and thus the discount factor is

negligible. We therefore set d = 0 for simplicity. Each app was introduced one observation

period after the launch of the previous one, so T = 1 for our dataset. In addition, we set P = 1 as a

normalization constant. This choice has the additional benefit that the improvement due to the

existence of the platform is in percentages. Given these assumptions, Equation 3 transforms as

follows:

(4) Platform Benefit (d=0 ,T=1 , P=1 )=ro (1−δ )( 11−δ r o

−ri

1−δ ro ri)

Appendix D details the equations and method used to estimate values for ri, ro, and δ, and

Table 4 summarized these results.

Our estimation shows a substantively high ro of 99.7%, implying that the publisher is

successful at retaining its customers. There might be two reasons for such a large retention: First,

we removed the first week data point from the estimation, as many of these “weeks” were in

effect only partial weeks. Second, in most apps (as in our data), retention rates in the first days

20

are very low due to the fact that many people download yet in fact do not play, and retention

rates stabilize thereafter (Grennan 2016; Haslam 2016). This phenomenon may be associated

with the ease of downloading an app, leading to a natural selection of users who find the app less

relevant for them (Chen 2016).

Table 4: Platform benefit sensitivity analysis for mobile games

Android iOS

Outside retention (ro) 99.7%

Internal retention (ri) 83.5%

Cross-promotion rate (1−ri) 16.5%

Product-related decline per period (δ) 49.0% 39.5%

Platform benefit (Equation 4) 27.6% 24.4%

Elasticity: % improvement per 1% of increased cross promotion (1−ri) 1.4% 1.3%

Elasticity: % improvement per 1% of increased external retention (ro) 0.7% 0.5%

Change in platform benefit if cross promotion decreases from 16.5% to

10%-9.9% -9.0%

Change in platform benefit if cross promotion increases from 16.5% to 20% +5.0% +4.6%

Table 4 shows that the platform benefit equals 27.6% increase in CLV in Android devices,

and 24.4% increase in CLV in iOS devices. Furthermore, using Equation (C1), we can see that

by increasing the cross-promotion effort by 1% (thus decreasing r iby 1%), the platform benefit

increases by 1.4% for Android and 1.3% for iOS games. Comparably, the elasticity toward ro,

given in Equation (D6) is smaller: 0.7% for Android, and 0.5% for iOS games. This suggests that

the publisher would benefit from increasing cross promotion over external retention. Finally, we

examine what would happen if the internal retention levels (r i) increased to 90%, thereby

reducing cross promotion to 10%. In that case, the platform benefit would decrease by 9.9% in

21

Android, and 9.0% in iOS. Similarly, reducing rito 80%, (meaning that cross promotion

increases to 20%) will increase the platform benefit by 5.0% in Android, and 4.6% in iOS.

Note that such changes can have a substantial effect on the firm’s profitability. Gaming

firms are often characterized by a large number of customers with low profitability, where often

the lifetime value is not much higher than the customer acquisition cost. Therefore, enhancing

CLV even by a few percent can result in notable gains in overall customer equity.

Discussion

The idea that firms should manage their offerings as product platforms that consist of

families of products with a common underlying logic, instead of as a collection of single

unrelated entities (Sawhney 1998) has been advocated for a while. Such a platform view, which

focuses on the process of identifying and exploiting commonalities among a firm’s various

offerings, has been notable in areas such as in strategy, technology, and new product

management (Mäkinen, Seppänen, and Ortt 2014; Thomas, Autio, and Gann 2014). The

marketing literature took a de facto platform approach when looking at issues such as brand

architecture and extension (Aaker and Joachimsthaler 2000), technological generations (Norton

and Bass 1987), and new product cannibalization (Heerde, Srinivasan, and Dekimpe 2010).

However, the implications for customer management have yet to be explored. The importance of

digital environments in which products can be easily connected and customers can be

individually targeted make this a relevant and timely issue.

There are certainly straightforward reasons to conduct cross promotion in a platform. If

one can convince users to consume two products at the same time rather than one, the benefit is

obvious. The same applies if one can convince users to move from a product with lower CLV to

22

one that is by nature more profitable. What we demonstrate in our analysis is that even in non-

trivial environments of similar products, the mere fact that products are introduced sequentially

in an environment of declining engagement creates incentives for customer transferal.

A first question that emerges in this context is when a decline in engagement can be

expected. As aforementioned, such decline depends on the product or on the customer. The

gaming industry may be largely characterized by declining temporal engagement, yet even this

overall trend does not apply to all games in the same manner. Some games differ in this respect,

and may even exhibit increasing engagement over time, for example due to the formation of

clans and groups in multi-user games. In some games, there will be differing segments of

players, some with declining engagement, and some with increasing engagement. Given the

ability to follow individual customers, game publishers can decide whom to target for cross

promotion based on players’ patterns of temporal engagement.

A second question, which we did not address, relates to the cost of cross promotion. One

could argue that the firm could use the space devoted to cross promotion for other types of

advertising, thus there is an opportunity cost to be considered. Another type of cost is customer

annoyance with cross-promotion activities (Goldstein et al. 2014), which may negatively impact

platform retention. Our analysis of platform benefit can thus be seen as a ceiling on the cost of

cross promotion: Cross promotion only creates value if the associated costs are below the

platform benefit.

Do we need a platform?

Our formal analysis focuses on the benefit of cross promotion, which is reflected in a

change in the level of the internal retention rate. One could also ask whether a platform creates

benefits for the firm by its mere presence, beyond any potential cross-promotion activities. As

23

we see from the platform benefit equation (Equation 3), under declining engagement, a

customer’s tendency to move among products (i.e., an internal retention rate r i of less than one),

which is enabled through interproduct connectivity, creates lifetime value benefits. Thus, even

without explicit cross-promotion activities aimed at changing that rate, the firm has an incentive

to enable customers to move easily among products. Increasing product compatibility, for

example by lowering switching costs through cross-product learning or connecting products

through in-game experiences can therefore be beneficial.

The case of external cross promotion

Our analysis focuses on internal cross promotion within platforms. The case of external

cross promotion across platforms is more complex, as it involves an outside party. Such an

outside party can either be another firm with whom customers are exchanged directly, or a

platform that manages the exchange among many companies. Regardless, the dynamics

presented for the internal cross promotion case help us to assess the benefit of external cross

promotion as well. Consider a case in which a firm has two similar products with declining

engagement that are consecutively launched. Assume that this firm has a cross-promotion

agreement under which it sends and receives customers to and from a third party. In the absence

of additional knowledge on the characteristics of the incoming customers, we assume that the

average profitability of incoming customers is similar to that of outgoing customers.

In such a case, the dynamics are similar to what we saw in the case of internal promotion:

The firm should cross promote its own customers from the first product, but promote itself

within the third party for the second (newer) product. Although it is not the same customer that is

moved from product to product, but rather different ones, we still expect to obtain similar

benefits as in the case of internal cross promotion. Of course, if the firm can assess in advance

24

the profitability of incoming customers and specifically target those with higher profitability for

cross promotion, the benefits realized will be even larger.

The social implications of cross promotion

As depicted in Table 1, the motivation for cross promotion can be the desire to create

direct engagement (and by consequence CLV), or the desire to create indirect engagement of

social value (Haenlein and Libai 2017). This logic mirrors the consensus that customer

engagement is reflected both in direct engagement, which impacts the level of usage and

purchases, and in indirect engagement, which represents social influence activities that affect the

profitability of others (Pansari and Kumar 2017). The effect of timing in this respect is notable.

In the case of mobile gaming, managers we interviewed stressed the importance of the game’s

appearing as early as possible on the ranking tables in the app store. App producers therefore

have a short window of opportunity in which to generate attention that will get them onto the

charts in the app stores (Kimura 2014; Rice 2013). Moving customers via cross promotion to a

game in its first week may therefore create relatively high social value in this regard.

Yet this logic also applies to other industries, as the social advantage of early customer

adoption has been acknowledged in a wider sense. First, Hogan, Lemon, and Libai (2003), for

example, demonstrated that an early lifecycle customer is worth more, as s/he helps to initiate the

snowball effect of new product social influence. This finding has been supported by evidence on

the power of early adopters on the diffusion of new products (Catalini and Tucker 2017).

Second, word of mouth often occurs more in the beginning of the customer-product relationship,

when a customer is enthused about his or her choice, and less so later (Doorn et al. 2010). Third,

customers use the product less over time (due to declining direct engagement), which results in

less WOM engagement (Kumar et al. 2010). Overall, past research suggests that the pattern of

25

the indirect social effect should be consistent with the direct effect that is our current focus.

Transferring customers may thus result not only in a platform benefit due to the change in direct

engagement, but also in a stronger social influence, which will create an indirect platform benefit

by affecting customer equity.

Transferring the best customers

Our analysis raises an interesting issue of the type of customer to whom a firm may wish to

cross promote. On the one hand, and as indicated in Proposition 2, customers with higher per-

period profitability – also called revenue leaders (Haenlein and Libai 2013) – are those that

create the most platform benefit. On the other hand, to maximize social influence and indirect

engagement, it could be wise to target customers with many social connections, or so-called

opinion leaders, as their ability to affect multiple others may create more value if they are

transferred to the next product.

Overall, the move from a single product to a platform view has fundamental implications

for our thinking on customer retention. In a single-product case, firms will want to invest much

in retaining their best customers. In a platform world, the best customers (be those revenue

leaders or opinion leaders) may best be transferred early on to maximize their contribution to the

next product. Although conceptually straightforward, this may not be simple to implement, as

products are often managed by separate brand managers who consider the success of their

individual product and are evaluated thereby. Because of this attachment, and due to sentimental

and political reasons, brand managers may be reluctant to “kill” a brand, even when necessary

(Yohn 2015). Moving the best customers to another product may therefore create resistance. A

shift to a platform view and citing the associated platform benefit is essential in this regard.

26

The case of multiple products

Given that our analysis has focused on a two-product platform, it is sensible to ask whether

the basic rationale can be expected to change if the firm has multiple products in the market.

Under declining engagement, the answer is quite straightforward: If one assumes similar

products in terms of profitability and declining engagement, then the most recent product in the

market will always be the most appealing one to which to move customers. For this product, the

engagement difference would be maximal, and the social impact due to the early lifecycle effect

would be stronger. Interestingly, this is precisely the strategy of many multi-product firms that

we were able to observe: The priority of cross promotion is to transfer customers to the newest

game. If this is not possible, the next newest game is considered, and so on, as we discuss in the

sensitivity analysis section and in Appendix D.

The customer acquisition dilemma

Our analysis has focused on the case of the lifetime value of a single customer, assuming

that s/he has already been acquired for Product 1. We therefore have not addressed customer

acquisition costs. Theoretically, the question of customer acquisition is independent of the

platform benefit analysis we conduct. A firm’s decision to increase customer equity by shifting

other customers to Product 2 is independent of optimizing the value of the customer who already

consumes Product 1.

Regardless, at least three issues should be taken into account: First, in practice, companies

have budget constraints that limit their spending decisions. Given that cross promotion is not

free, the cost and benefit of acquiring new customers vs. those acquired via cross promotion

should be compared. Second, firms often assess their investment in customer acquisition by

comparing it to the lifetime value of a customer. In a platform world, the probability of moving

27

among products and the extra lifetime value created needs to be taken into account. This leads to

more complex decision making in the acquisition-retention area, as there are two kinds of

retention investment (internal and outside) that have to be considered. Third, if the social benefits

of cross promotion are included, then customer acquisition efforts matter directly. The social

benefit of cross promotion stems from the effect of other customers, and in a social context, their

number matters greatly. One reason that early-on customers have a higher social value is that

there are few other customers (Hogan, Lemon, and Libai 2003). The more customers acquired

early on, the smaller the social contribution of cross promotion.

To appreciate the nature of managing customers in a product platform, one can look at the

situation of a game publisher that we interviewed for this research. This company introduces

dozens of games a year and depends heavily on cross promotion in which games push each

other. The firm actively builds on both direct and indirect cross-promotion effects, and thinks a

great deal about how to create cross-promotion activities among the products that are in the

market, and how much their effort should be divided among cross-promotion activities and new

customer acquisition. Our analysis is just one step in helping such managers to understand the

complex environment of multi-product platforms. Using a simple model, we highlight a number

of issues that can serve as a basis for further research. For a given firm, the best solution may be

to build a decision support agent-based model that will help to manage the market complexities

via simulations (Chica and Rand 2017). In a more general sense, more research is needed that is

aimed at adapting our knowledge from a single-product approach to that of a platform.

28

Appendix A: Retention and Upgrade Probabilities for Declining Profit

For simplicity, we assume T = 1, P = 1, and d = 0. This implies that at period T = 1, the

consumer is playing with Game 1, and Game 2 is introduced, and that there is no discounting.

We observe the transition probabilities from Game 1 to Game 2 as depicted in Table 3.

Table A1: Retention and Upgrade Probabilities (Constant Per-Period Profit)

Period (from T+1) 1 2 3

Game 1 ro r i ro2 r i r i ¿ ro

2 ri2 ro

3 r i2 ri=r o

3 r i3

Game 2 ro(1−r¿¿ i)¿ ro2 r i(1−r¿¿ i)¿ ro

3 r i2(1−r¿¿ i)¿

ro2(1−r¿¿ i)¿ ro

3 ri(1−r¿¿ i)¿

ro3(1−r¿¿ i)¿

Sum of Game 2

probabilitiesro

2(1−r¿¿ i)(1+r i )=¿¿

ro2(1−ri

2)

ro3(1−ri

3)

Table A2: Retention and Upgrade Probabilities (Product-related Decline)

Period (from T+1) 1 2 3

Game 1 ro r i δr o2 ri

2 δ 2r o3 r i

3

Game 2 ro(1−r¿¿ i)¿ δr o2 r i(1−r¿¿i)¿ δ 2r o

3 r i2(1−r¿¿ i)¿

δr o2(1−r¿¿ i)¿ δ 2r o

3 r i(1−r¿¿ i)¿

δ 2r o3 (1−r¿¿ i)¿

Sum of Game 2

probabilitiesδ ro

2(1−r i2) δ 2r o

3 (1−r i3)

29

Table A2: Retention and Upgrade Probabilities (Consumer-related Decline)

Period (from T+1) 1 2 3

Game 1 ro r i δr o2 ri

2 δ 2r o3 r i

3

Game 2 ro(1−r¿¿ i)¿ ro2 ri(1−r¿¿ i)¿ ro

3 r i2(1−r¿¿ i)¿

δr o2(1−r¿¿ i)¿ δr o

3 r i(1−r¿¿i)¿

δ 2r o3 (1−r¿¿ i)¿

Sum of Game 2

probabilitiesro

2(1−r¿¿ i)(δ+r i)¿ro3 (1−r i )(δ 2+δ ri+r i

2)

It follows that the value generated by Product 2 in Period T + k is equal to:

(A1) Value Product 2 (product-related decline | t = k) = δ k−1r ok (1−ri

k)

This is the same as the corresponding cell of Table 3 in the text, with d = 0 and T = P = 1.

Summing over k yields:

(A2) CLV Product 2 (product-related decline) = ∑k =1

∞

(1−rik) δ

k−1ro

k

On the other hand, with consumer-related decline, we have:

(A3) Value Product 2 (consumer-related decline | t = k) = rok (1−ri)∑

j=1

k

r ij−1 δk− j

Summing over k yields:

(A4) CLV Product 2 (consumer-related decline) = (1−ri)∑k=1

∞

∑j=1

k

rok ri

j−1δ k− j

We next show the following proposition:

Proposition A: CLV (consumer-related decline) is always greater than CLV (product-

related decline), if

In order to prove Proposition A, we will show that Value Product 2 (consumer-related decline | t

= k) is greater than Value Product 2 (product-related decline | t = k) if δ <1. As this holds for all

k, summing over k yields the proposition. To show this, observe the following strings of

equations, where the inequality results from the fact that δ <1:

30

CLV (consumer-related decline | t = k) = (1−ri )∑j=1

k

r0k r i

j−1 δk − j>¿

(1−ri )∑j=1

k

rok r i

j−1 δ k−1=rok δ k−1 (1−ri )∑

j=1

k

r ij−1=ro

k δk−1 [∑j=1

k

rij−1−r i∑

j=1

k

rij−1]=ro

k δ k−1(1−r ik ) = CLV

(product-related decline | t = k)

Appendix B: Calculating Platform Benefit

The CLV of a customer within a platform has three components: (1) the value from the

consumption of Product 1 between Period 1 and Period T; (2) the value from the consumption of

Product 1 between Period T+1 and infinity, and (3) the value from the consumption of Product 2

between Period T+1 and infinity.

The first component, value from consuming Product 1 between 1 and T, is equal to:

(B1) CLV 1 ,1 → T=P

1+d+Pδ

r o

(1+d )2+…+P δT −1 ro

T −1

(1+d )T

which can be simplified to:

(B2) CLV 1 ,1 → T=P

1+d

1−( δ ro

1+d )T

1−δ ro

1+d

= P1+d−δ ro [1−( δ r o

1+d )T ]

Note that this is the standard CLV of a product, adjusted for a finite horizon T.

The second component, value from Product 1 between T+1 and infinity, is:

(B3) CLV 1 ,T +1 → ∞=P δ T roT r i

(1+d )T +1 +P δT +1 roT +1r i

2

(1+d )T +2 +…

which can be simplified to:

(B4) CLV 1 ,T +1 → ∞=P δT roT r i

(1+d )T +11

1−δ r or i

1+d

=P( δ ro

1+d )T ri

1+d−δ ro r i

The third term, value from Product 2 between T+1 and infinity, is:

(B5) CLV 2 , T+1 → ∞=P¿¿¿

Breaking down each term (1−rik) into its two parts (1 and −ri

k), this can be simplified to:

(B6) CLV 2 , T+1 → ∞=P( ro

1+d )T

( 11+d−δ ro

−ri

1+d−δ r o ri)

31

Summing up Equations (B2), (B4), and (B6) leads to the CLV of a customer within the platform:

(B7) CLV 1+2=P

1+d−δ r o+P( ro

1+d )T

( 1−δ T )( 11+d−δ ro

−r i

1+d−δ ro ri)

It is straightforward to see from Equation (B7) that the CLV of a customer within the platform is

equal to the CLV from the consumption of Product 1 between Period 1 and infinity (first term)

plus the gain that stems from the platform (second term). We therefore define the net benefit of

the platform as the second term in Equation (B7), which is given in Equation (3) in the text.

32

Appendix C: The Value of Cross Promotion

Since r i represents internal retention rate, cross-promotion is equivalent to 1−ri.

Derivative of Platform Benefit with respect to cross promotion 1−ri

(C1)∂ PB

∂(1−ri)=−∂ PB

∂ r i=P ( r o

1+d )T

(1−δ T ) 1+d(1+d−δ ro ri )

2 ≥ 0 if δ ≤ 1.

Derivative of ∂ PB /∂(1−ri) with respect to r i, ro, P, and δ

(C2)∂2 PB

∂(1−ri)∂ ri=P( r o

1+d )T

(1−δT ) 2(1+d )δ ro

(1+d−δ ro r i )3 ≥ 0 if δ ,r i , ro ≤1.

(C3)∂2 PB

∂(1−ri)∂ ro=P( ro

1+d )T −1

(1−δT ) T (1+d−δ ro ri)+2δ r o ri

(1+d−δ ro r i )3 ≥ 0 if δ ,r i , ro ≤1.

(C4)∂2 PB

∂(1−ri)∂ P=( ro

1+d )T

(1−δT ) 1+d(1+d−δ r ori )

2 ≥0 if δ ≤ 1.

(C5) ∂2 PB∂(1−ri)∂ δ

=−P ( r o

1+d )T

(1+d )[ (1+d ) T δT−δ (2+(T−2 ) δ T )ri ro]

δ(1+d−δ ri ro)3

For Equation C5, it is straightforward to numerically demonstrate the inverse-U-shape of this

function.

33

Appendix D: Details on the Data-Based Sensitivity Analysis

We use the data from the publisher to get a measure for two of our parameters: ro, and ri. We

examine the first cohort of each app, i.e., we follow the retention of those who adopted App1 on

the day it was launched (T = 1). We denote x¿ as the number of users at Period t in App i (i:1, 2,

3, 4), and use the number of users that organically adopted App1 in the first week as a constant

(x11). In the second week (or T+1 for the following apps), in App1, x1o∙ro∙ri, users remain, as

x1o∙(1-ro) have left the publisher completely and x1o∙(1-ri) left for App2. This dynamic is similar to

the one shown in Game 1 dynamics of Table A1 that present the retention probabilities in the

periods following the initial adoption. Similarly, x1t, the number of users in the first app in Period

t, can be modeled as:

(D1) x1 t=x11 rot−1ri

t −1

The second app starts at the second period, and some users, denoted asx2o, have adopted

organically, regardless of how many App1 users are cross promoted. Furthermore, another share

of users has arrived, via cross promotion from the first app (x1 o(1−ri)ro, in a manner similar to

Game 2 dynamics shown in Table A1, so that the observed number of users of App2 in Period 2

(the first period of App2) is:

(D2) x22=x2o+ x11 (1−r i)ro

In a similar manner, the observed number of users of App3 and App4 in their first relative

periods (Period 3 and Period 4 respectively), are driven by both organic and cross-promotion

adoptions. The number of organic adopters, i.e., those who arrive to the app in the first respective

period, are denoted as x io. Thus, the total number of users of App i in its introduction period,

Period i (e.g., Period 3 for App 3, Period 4 for App 4), can be denoted as xii.

(D3) x33=x3o+x22 (1−r i ) r o+x11 (1−ri ) r ir o

2

(D4) x44=x4o+x33 (1−r i ) ro+x22 (1−ri ) r i ro

2+x11( 1−ri ) r i2 ro

3

Note that in Equations (D3) and (D4), we assume that when there are more than two apps in the

market, the cross promotion is always directed at the most recent app to have entered the market.

This assumption fits the actual strategy that the publisher took in introducing these apps, but

could easily be adapted to any other mixture of app cross promotion.

Now we can write the general form for the number of adopters of App i in Period t:

34

(D5) x¿= xii rot−i ri

t−i

In the dataset, x11 is exogenous, yet we need to estimate x2o, x3

o, x4o, r i ,and ro. To do so, we

minimize the sum-of-squares difference, using the simulated annealing method for our parameter

evaluations, fitted via the GenSA function in the GenSA R package (Xiang et al. 2013). We

remove the first week data point from the estimation, as in most apps (as in our data), there is a

sharp drop in retention rates in the first week, and the retention rates stabilize thereafter (Grennan

2016; Haslam 2016). This phenomenon may be associated with the ease of download of an app,

leading to a natural selection of users who find the app less relevant for them (Chen 2016). R2

values are high and ranged from 93.3% in App1 to 96.4% in App3. The estimated values were ro

= 0.997 and ri = 0.835 (average values of goodness of fit across apps were: R2 = 94.6%, RMSE =

10,122, MAPE = 17.2%).

One more measure we are missing is the estimation of the product-related decline (δ). As the

publisher’s data are aggregate and do not include any information on the actual time each user

spent on the apps, but rather only the number of users per period, we turn to an external source to

evaluate δ. Fortunately, in 2016, Adjust, a mobile marketing research firm, released various key

performance indices of mobile apps (Adjust.com 2016). This report also included the average

time spent per user in an app over the first 30 days of the app’s life per category. To keep the

periods similar, we consider the usage levels in the same periods as in the publisher’s data.

We then estimate a simple decline model, following the dynamic from Table A2, where in each

period, usage declines by δ, with a functional power form of ut, and usage at Period t equals

ut=u1 δt−1. The estimated values were δAndroid = 0.49 (R2 = 89%, RMSE = 0.1, MAPE = 32.4%),

and δiOS = 0.40 (R2 = 92%, RMSE = 0.09, MAPE = 41.3%).

Finally, to compare the elasticity of (1-ri) and ro, we calculate the partial derivative of the

platform benefit with respect to the external retention rate. This is a relatively complex

expression, which we report in Equation (D6) below for reference only:

(D6)

∂ PB∂ ro

=P (1−δT )( ro

1+d )T [δ(( 1

1+d−δ r o )2

−( r i

1+d−δ r or i)

2

)+ Tro

( 11+d−δ r o

−r i

1+d−δ r ori) ]

35

References

Aaker, David A. and Erich Joachimsthaler (2000), "The Brand Relationship Spectrum: The Key to the Brand Architecture Challenge," California Management Review, 42 (4), 8 - 23.

Adjust.com (2016), "Mobile Benchmarks Q3 2016," in https://www.adjust.com/resources/insights/mobile-benchmarks-q3-2016/.

Ascarza, Eva, Raghuram Iyengar, and Martin Schleicher (2016), "The Perils of Proactive Churn Prevention Using Plan Recommendations: Evidence from a Field Experiment," Journal of Marketing Research, 53 (1), 46 - 60.

Ascarza, Eva, Scott Neslin, Oded Netzer, Zachery Anderson, Peter Fader, Sunil Gupta, Bruce Hardie, Aurelie Lemmens, Barak Libai, David Neal, Foster Provost, and Rom Y. Schrift (2017), "In Pursuit of Enhanced Customer Retention Management," SSRN.

Catalini, Christian and Catherine Tucker (2017), "When Early Adopters Don't Adopt," Science, 357 (6347), 135 - 36.

Chen, Andrew (2016), "New Data Shows Losing 80% of Mobile Users Is Normal, and Why the Best Apps Do Better," in http://andrewchen.co/new-data-shows-why-losing-80-of-your-mobile-users-is-normal-and-that-the-best-apps-do-much-better/.

Chica, Manuel and William Rand (2017), "Building Agent-Based Decision Support Systems for Word-of-Mouth Programs: A Freemium Application," Journal of Marketing Research, 54 (5), 752 - 67.

Chupa Team (2015), "Cross-Promoting Apps: The Secret to a Successful Portfolio of Casual Games," in http://www.chupamobile.com/blog/2015/07/10/cross-promoting-apps-the-secret-to-a-successful-portfolio-of-casual-games/.

Danaher, Peter J., Bruce G. S. Hardie, and William P. Jr. Putsis (2001), "Marketing-Mix Variables and the Diffusion of Successive Generations of a Technological Innovation," Journal of Marketing Research, 38 (4), 501 - 14.

Dhar, Tirtha, Guanghui Sun, and Charles B. Weinberg (2012), "The Long-Term Box Office Performance of Sequel Movies," Marketing Letters, 23 (1), 13 - 29.

Doorn, Jenny van, Katherine N. Lemon, Vikas Mittal, Stephan Nass, Doreen Pick, Peter Pirner, and Peter C. Verhoef (2010), "Customer Engagement Behavior: Theoretical Foundations and Research Directions," Journal of Service Research, 13 (3), 253 - 66.

Dowling, Grahame (2002), "Customer Relationship Management: In B2c Markets, Often Less Is More," California Management Review, 44 (3), 87 - 104.

Entertainment Software Association (2017), "Essential Facts About the Computer and Video Game Industry," in http://www.theesa.com/wp-content/uploads/2017/09/EF2017_Design_FinalDigital.pdf.

Fader, Peter S. and Bruce G.S. Hardie (2010), "Customer-Base Valuation in a Contractual Setting: The Perils of Ignoring Heterogeneity," Marketing Science, 29 (1), 85 - 93.

36

Goldstein, Daniel G., Siddharth Suri, R. Preston McAfee, Matthew Ekstrand-Abueg, and Fernando Diaz (2014), "The Economic and Cognitive Costs of Annoying Display Advertisements," Journal of Marketing Research, 51 (6), 742–52.

Grennan, Todd (2016), "Less Than 25% of New App Users Return the Day after First Use (Here’s What to Do About It)," in https://www.braze.com/blog/app-customer-retention-spring-2016-report/.

Gruner, Stephanie L. (1997), "The Secrets of Cross-Promotion," in https://www.inc.com/magazine/19970601/1259.html.

Gupta, Sunil, Dominique Hanssens, Bruce Hardie, Wiliam Kahn, V. Kumar, Nathaniel Lin, Nalini Ravishanker, and S. Sriram (2006), "Modeling Customer Lifetime Value," Journal of Service Research, 9 (2), 139 - 55.

Gupta, Sunil, Donald R. Lehmann, and Jennifer Ames Stuart (2004), "Valuing Customers," Journal of Marketing Research, 41 (1), 7 - 18.

Haenlein, Michael (2017), "How to Date Your Clients in the 21st Century: Challenges in Managing Customer Relationships in Today's World," Business Horizons, 60 (5), 577 - 86.

Haenlein, Michael and Andreas M. Kaplan (2009), "Unprofitable Customers and Their Management," Business Horizons, 52 (1), 89 - 97.

Haenlein, Michael, Andreas M. Kaplan, and Detlef Schoder (2006), "Valuing the Real Option of Abandoning Unprofitable Customers When Calculating Customer Lifetime Value," Journal of Marketing, 70 (3), 5 - 20.

Haenlein, Michael and Barak Libai (2017), "Seeding, Referral and Recommendation: Creating Profitable Word-of-Mouth Programs," California Management Review, 59 (2), 68 - 91.

Haenlein, Michael and Barak Libai (2013), "Targeting Revenue Leaders for a New Product," Journal of Marketing, 77 (3), 65 - 80.

Haslam, James (2016), "Retention Rates: A Deeper Look at the Benchmarks," in https://www.adjust.com/blog/retention-rates-a-deeper-look/.

Heerde, Harald J. van, Shuba Srinivasan, and Marnik G. Dekimpe (2010), "Estimating Cannibalization Rates for Pioneering Innovations," Marketing Science, 29 (6), 1024 - 39.

Hogan, John E., Katherine N. Lemon, and Barak Libai (2003), "What Is the True Value of a Lost Customer?," Journal of Service Research, 5 (3), 196 - 208.

Hwong, Connie (2016), "The Average Mobile Game Day," in http://www.vertoanalytics.com/average-mobile-game-day/.

Johnson, Michael D., Andreas Herrmann, and Frank Huber (2006), "The Evolution of Loyalty Intentions," Journal of Marketing, 70 (2), 122 - 32.

Kahn, Barbara E. (1995), "Consumer Variety-Seeking among Goods and Services: An Integrative Review," Journal of Retailing and Consumer Services, 2 (3), 139 - 48.

Kim, Hyeongmin (Christian) (2013), "How Variety-Seeking Versus Inertial Tendency Influences the Effectiveness of Immediate Versus Delayed Promotions," Journal of Marketing Research, 50 (3), 416–26.

37

Kimura, Hugh (2014), "Why App Store Keyword Rankings Drop Dramatically Seven Days after Launch," in https://sensortower.com/blog/why-app-store-keyword-rankings-drop-dramatically-seven-days-after-launch.

Klingebiel, Ronald and Christian Rammer (2014), "Resource Allocation Strategy for Innovation Portfolio Management," Strategic Management Journal, 35 (2), 246 - 68.

Klotzbach, Chris (2016), "Enter the Matrix: App Retention and Engagement," in http://flurrymobile.tumblr.com/post/144245637325/appmatrix.

Knott, Aaron, Andrew Hayes, and Scott A. Neslin (2002), "Next-Product-to-Buy Models for Cross-Selling Applications," Journal of Interactive Marketing, 16 (3), 59 - 75.

Kumar, V., Lerzan Aksoy, Bas Donkers, Rajkumar Venkatesan, Thorsten Wiesel, and Sebastian Tillmanns (2010), "Undervalued or Overvalued Customers: Capturing Total Customer Engagement Value," Journal of Service Research, 13 (3), 297 - 310.

Kumar, V., Morris George, and Joseph Pancras (2008), "Cross-Buying in Retailing: Drivers and Consequences," Journal of Retailing, 84 (1), 15 - 27.

Kumar, V. and Anita Pansari (2015), "Aggregate and Individual-Level Customer Lifetime Value," in Handbook of Research on Customer Equity in Marketing, V. Kumar and Danish Shah, eds.

Kumar, V., Girish Ramani, and Timothy Bohling (2004), "Customer Lifetime Value Approaches and Best Practice Applications," Journal of Interactive Marketing, 18 (3), 60 - 72.

Kumar, V. and Denish Shah (2015), Handbook of Research on Customer Equity in Marketing: Elgar.

Kumar, V., Rajkumar Venkatesan, Tim Bohling, and Denise Beckmann (2008), "The Power of Clv: Managing Customer Lifetime Value at Ibm," Marketing Science, 27 (4), 585 - 99.

Landsman, Vardit and Stefan Stremersch (2011), "Multihoming in Two-Sided Markets: An Empirical Inquiry in the Video Game Console Industry," Journal of Marketing, 75 (6), 39 - 54.

Li, Shibo, Baohong Sun, and Alan L. Montgomery (2011), "Cross-Selling the Right Product to the Right Customer at the Right Time," Journal of Marketing Research, 48 (4), 683 - 700.

Luckerson, Victor (2015), "This Is How Many Apps You’re Really Using on Your Smartphone," in http://fortune.com/2015/09/24/apps-smartphone-facebook/.

Mahajan, Vijay and Eitan Muller (1996), "Timing, Diffusion, and Substitution of Successive Generations of Technological Innovations: The Ibm Mainframe Case," Technological Forecasting and Social Change, 51 (2), 109 - 32.

Mäkinen, Saku J., Marko Seppänen, and J. Roland Ortt (2014), "Introduction to the Special Issue: Platforms, Contingencies and New Product Development," Journal of Product Innovation Management, 31 (3), 412 - 16.

Mark, Tanya, Katherine N. Lemon, Mark Vandenbosch, Jan Bulla, and Antonello Maruotti (2013), "Capturing the Evolution of Customer–Firm Relationships: How Customers Become More (or Less) Valuable over Time," Journal of Retailing, 89 (3), 231 - 45.

38

McDonald, Emma (2017), "The Global Games Market Will Reach $108.9 Billion in 2017 with Mobile Taking 42%," in https://newzoo.com/insights/articles/the-global-games-market-will-reach-108-9-billion-in-2017-with-mobile-taking-42/.

Min, Sungwook, Xubing Zhang, Namwoon Kim, and Rajendra K. Srivastava (2016), "Customer Acquisition and Retention Spending: An Analytical Model and Empirical Investigation in Wireless Telecommunications Markets," Journal of Marketing Research, 53 (5), 728 - 44.

Musalem, Andrés and Yogesh V. Joshi (2009), "How Much Should You Invest in Each Customer Relationship? A Competitive Strategic Approach," Marketing Science, 28 (3), 555 - 65.

Nelson, Randy (2016), "Apple's App Store Will Hit 5 Million Apps by 2020, More Than Doubling Its Current Size," in https://sensortower.com/blog/app-store-growth-forecast-2020.

Norton, John A. and Frank M. Bass (1987), "A Diffusion Theory Model of Adoption and Substitution for Successive Generations of High-Technology Products," Management Science, 33 (9), 1069 - 86.

Oestreicher-Singer, Gal, Barak Libai, Liron Sivan, Eyal Carmi, and Ohad Yassin (2013), "The Network Value of Products," Journal of Marketing, 77 (3), 1 - 14.

Pansari, Anita and V. Kumar (2017), "Customer Engagement: The Construct, Antecedents, and Consequences," Journal of the Academy of Marketing Science, 45 (3), 294 - 311.

Peres, Renana, Eitan Muller, and Vijay Mahajan (2010), "Innovation Diffusion and New Product Growth Models: A Critical Review and Research Directions," International Journal of Research in Marketing, 27 (2), 91 - 106.

Perez, Sarah (2016), "App Store to Reach 5 Million Apps by 2020, with Games Leading the Way," in https://techcrunch.com/2016/08/10/app-store-to-reach-5-million-apps-by-2020-with-games-leading-the-way/.

Prins, Remco and Peter C. Verhoef (2007), "Marketing Communication Drivers of Adoption Timing of a New E-Service among Existing Customers," Journal of Marketing, 71 (2), 169 - 83.

Reichheld, Frederick F. and W. Earl Jr. Sasser (1990), "Zero Defections: Quality Comes to Service," Harvard Business Review, 68 (5), 105 - 11.

Reichheld, Frederick F. and Phil Schefter (2000), "E-Loyalty: Your Secret Weapon on the Web," Harvard Business Review, 78 (4), 105 - 13.

Reinartz, Werner J. and V. Kumar (2000), "On the Profitability of Long-Life Customers in a Noncontractual Setting: An Empirical Investigation and Implications for Marketing," Journal of Marketing, 64 (4), 17 - 35.

Rice, Kelley (2013), "Why Pre-Launch Hype Is the Key to App Success," in https://www.kinvey.com/why-pre-launch-hype-is-the-key-to-app-success/.

Sajeesh, S. and Jagmohan S. Raju (2010), "Positioning and Pricing in a Variety Seeking Market," Management Science, 56 (6), 949 - 61.

Sawhney, Mohanbir S. (1998), "Leveraged High-Variety Strategies: From Portfolio Thinking to Platform Thinking," Journal of the Academy of Marketing Science, 26 (1), 54 - 61.

39

Schmitz, Christian, You-Cheong Lee, and Gary L. Lilien (2014), "Cross-Selling Performance in Complex Selling Contexts: An Examination of Supervisory- and Compensation-Based Controls," Journal of Marketing, 78 (3), 1 - 19.

Schweidel, David A., Peter S. Fader, and Eric T. Bradlow (2008), "A Bivariate Timing Model of Customer Acquisition and Retention," Marketing Science, 27 (5), 829 - 43.

Seetharaman, P. B. and Hai Che (2009), "Price Competition in Markets with Consumer Variety Seeking," Marketing Science, 28 (3), 516 - 25.

Shah, Denish, V. Kumar, Yingge Qu, and Sylia Chen (2012), "Unprofitable Cross-Buying: Evidence from Consumer and Business Markets," Journal of Marketing, 76 (3), 78 - 95.

Shin, Jiwoong, K. Sudhir, and Dae-Hee Yoon (2012), "When to “Fire” Customers: Customer Cost-Based Pricing," Management Science, 58 (5), 932 - 47.

Sriram, S., Pradeep K. Chintagunta, and Manoj K. Agarwal (2010), "Investigating Consumer Purchase Behavior in Related Technology Product Categories," Marketing Science, 29 (2), 291 - 314.

Sviokla, John and Anthony J. Paoni (2005), "Every Product's a Platform," Harvard Business Review, 83 (10), 17 - 18.

Thomas, Llewellyn D. W., Erkko Autio, and David M. Gann (2014), "Architectural Leverage: Putting Platforms in Context," Academy of Management Perspectives, 28 (2), 198 - 219.

Thota, Sweta Chaturvedi and Abhijit Biswas (2009), "I Want to Buy the Advertised Product Only!: An Examination of the Effects of Additional Product Offers on Consumer Irritation in a Cross-Promotion Context," Journal of Advertising, 38 (1), 123 - 36.

Umashankar, Nita, Yashoda Bhagwat, and V. Kumar (2017), "Do Loyal Customers Really Pay More for Services?," Journal of the Academy of Marketing Science, 45 (6), 807 - 26.

Vaghari, David (2017), "The 6 Keys to Flawless Internal Cross Promotions," in http://blog.upsight.com/blog/the-6-keys-to-flawless-internal-cross-promotions.

Verhoef, Peter C. (2003), "Understanding the Effect of Customer Relationship Management Efforts on Customer Retention and Customer Share Development," Journal of Marketing, 67 (4), 30 - 45.

Wong, Steven (2016), "How Disney Mobile Is Crossing into the Future of Entertainment," in http://www.alistdaily.com/strategy/disney-mobile-gaming-crosses-future-entertainment/.

Xiang, Y., S. Gubian, B. Suomela, and J. Hoeng (2013), "Generalized Simulated Annealing for Global Optimization: The Gensa Package," R Journal, 5 (1).

Yohn, Denise Lee (2015), "Know When to Kill Your Brand," in https://hbr.org/2015/07/know-when-to-kill-your-brand.

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