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Peer influence in network markets: a theoretical and empirical analysis

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Abstract

Network externalities spur the growth of networks and the adoption of network goods in two ways. First, they make it more attractive to join a network the larger its installed base. Second, they create incentives for network members to actively recruit new members. Despite indications that the latter “peer effect” can be more important for network growth than the installed-base effect, it has so far been largely ignored in the literature. We address this gap using game-theoretical models. When all early adopters can band together to exert peer influence—an assumption that fits, e.g., the case of firms supporting a technical standard—we find that the peer effect induces additional growth of the network by a factor. When, in contrast, individuals exert peer influence in small groups of size n, the increase in network size is by an additive constant—which, for small networks, can amount to a large relative increase. The difference between small, local, personal networks and large, global, anonymous networks arises endogenously from our analysis. Fundamentally, the first type of networks is “tie-reinforcing,” the other, “tie-creating”. We use survey data from users of the Internet services, Skype and eBay, to illustrate the main logic of our theoretical results. As predicted by the model, we find that the peer effect matters strongly for the network of Skype users—which effectively consists of numerous small sub-networks—but not for that of eBay users. Since many network goods give rise to small, local networks, our findings bear relevance to the economics of network goods and related social networks in general.

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Notes

  1. The studies by Domingos and Richardson (2001) and Subramani and Rajagopalan (2003) are two exceptions published in the field of computing and information systems. The latter article in particular addresses, in a conceptual model, the motives of network members to recruit further adopters.

  2. With some simplification, Skype works in the following way. After registering with the Skype service, a user builds her personal contact list by sending contact requests to other users, or receiving and accepting requests herself. She can then call each person on her personal contact list via Skype. Calls are transmitted over the internet, and are free of charge for both parties. The Skype software also include other features such as conference calls, calls to fixed-line phones (SkypeOut), sending SMS or Instant Messaging. In September 2005, Skype was acquired by the Internet auction provider eBay.

  3. See http://about.skype.com/ (accessed June 9, 2011).

  4. See http://www.sec.gov/Archives/edgar/data/1498209/000119312511056174/ds1a.htm#rom83085_9 (accessed June 9, 2011).

  5. See http://www.skype.com/intl/en-us/tell-a-friend/ (accessed June 9, 2011).

  6. Word-of-mouth communication is a much researched topic in marketing and communication research. For an early work in the field of communication research see Lazarsfeld et al. (1944), who introduce the distinction between word-of-mouth communication and mass media influence in the context of voter behavior. For an early contribution in the field of marketing see Arndt (1967), who analyzes the effect of word-of-mouth communication on the diffusion of a new product in an experimental setting.

  7. To model this situation, one would have to determine how exactly peer influence is exerted on a person who would take the same action out of her own account. For the purpose of the current analysis, however, this question can remain unanswered. What matters is that up to a certain network size both effects can work concurrently, while beyond this size only the peer effect is relevant.

  8. In real life, it is a plausible situation that a network starts out as an insider tip among friends with growth largely through peer influence, while later it becomes popular and further adopters join because of the installed-base effect. However, this scenario is characterized by various overlaying effects, not all of which are captured in our models: the peer effect, the installed-base effect, and the effect of popularity. Popularity of a network good implies that information about it becomes more readily available and may even be impossible to ignore, which increases the perceived benefits and reduces the cost of adoption for all not-yet-adopters. This “popularity” effect is not captured in our models, though.

  9. We use the term “consumer” to keep the presentation simple. However, the potential adopters of the focal good may also be firms or other institutions.

  10. In fact, monotonicity of u(x) need not be assumed. Since each consumer is characterized only by the standalone utility she derives from the good, we are free to assign values of x in such a way to the consumers that their standalone utility decreases with x. Thus, we obtain \(u'(x) \le 0\) by definition rather than by assumption.

  11. A third possibility would be that the function equals zero at one or more points and is negative otherwise. These roots would constitute equilibria which are unstable against deviations to lower values of y. We refrain from pursuing this case further since we focus on stable equilibria.

  12. A solution y to Eq. 1 at which the sign changes from negative to positive would mean that, after a small deviation to \(y - \epsilon < y\), the marginal consumer would experience a negative net utility and would hence not join the network, reducing its size further. In contrast, a positive deviation of the network size to \(y + \epsilon \) would imply that the marginal non-consumer would derive a positive utility from joining the network. She would consequently do so and increase the network size further.

  13. That is, they have realistic expectations concerning the adoption that will take place in stage one, but are myopic with regard to peer effects coming into play in stage two. Without this assumption, some agents who do adopt in the base case would refrain from doing so, because they do better by deferring their adoption until the second stage, thus not being an influencer. We will relax the assumption later on that each early adopter becomes an influencer in stage two.

  14. After they have gone through the adoption process they might, in a third stage, act as influencers themselves. However, we restrict our analysis here to two stages. An extension to three or more stages would of course be feasible. However, if one aims at making the temporal structure more realistic, then a more suitable choice would be to introduce continuous time instead of three or more stages. We refrain from pursuing this approach in order to keep the model tractable.

  15. Of course, our model is a simplification of this scenario by allowing only two levels of communication intensity: either two individuals belong to the same network or they do not. We also abstract from the fact that some individuals will belong to more than one sub-network.

  16. The high degree of consistency of the three intersection points for each of the two services can be quantified using vector algebra. Consider, for the case of eBay, the line ending at the upper corner, denoted line P for “peer influence.” Normalizing the length of line P to unity, its intersection with line L is at 0.241 while that with line G is at 0.190. The difference thus equals 0.051, or 5.1 % of the length of line P. In an analogous way, the normalized differences between the two intersections obtains as \(0.266 - 0.211 = 0.055\) for line L, and as \(0.585 - 0.510 = 0.075\) for line G. For the case of Skype, the normalized differences are 0.086 (P), 0.082 (L), and 0.033 (G).

  17. This variable is operationalized as follows. 1: None of my friends or colleagues had told me about Skype (Ebay) and its features; 2: One or more of my friends or colleagues had told me about Skype (eBay) and its features; 3: One or more of my friends or colleagues had invited me to register with Skype (eBay); 4: One or more of my friends or colleagues had tried to persuade me to register with Skype (eBay); and 5: One or more of my friends or colleagues had pressed me to register with Skype (eBay).

  18. This variable is operationalized as follows. 1: I have not told any of my friends or colleagues about Skype (eBay) and its features; 2: I have told one or more of my friends or colleagues about Skype (eBay) and its features; 3: I have invited one or more of my friends or colleagues to register with Skype (eBay); 4: I have tried to persuade one or more of my friends or colleagues to register with Skype (eBay); 5: I have pressed one or more of my friends or colleagues to register with Skype (eBay).

  19. We caution the reader that a platform such as Facebook is far more complex than the relatively simple network services of Skype and eBay that we used as illustrations. Thus, one has to be careful in applying our result to this case. Still, despite many differences the three services share fundamental characteristics, and our theoretical analysis is kept in general terms. We thus think that the underlying mechanisms at work are robust.

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Acknowledgments

We are grateful to many people who shared their insights or commented on earlier drafts of the paper. Special thanks go to Nicoletta Corrocher, Oliver Fabel, Paul A. Kattuman, Tobias Kretschmer, Thomas Rønde, and Catherine Tucker. We also thank participants at seminars at the Academy of Management Meeting, Bocconi University, Deutsches Institut für Wirtschaftsforschung (DIW), the DRUID conference, the European Academy of Management, the TUM/LMU TIME colloquium, and the VfS Industrial Organization Divsion. Errors and oversights are ours alone.

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Authors and Affiliations

  1. TUM School of Management, Technische Universität München, Arcisstr. 21, 80333, Munich, Germany

    Joachim Henkel

  2. Center for Economic Policy Research (CEPR), London, UK

    Joachim Henkel

  3. Department of Business Administration, Universität Trier, Universitätsring 15, 54296, Trier, Germany

    Jörn Block

  4. Department of Applied Economics, Erasmus University Rotterdam, Rotterdam, Netherlands

    Jörn Block

  5. Technische Universität München, TUM School of Management, Munich, Germany

    Jörn Block

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  1. Joachim Henkel
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Appendix

Appendix

1.1 Symbols

c :

Variable cost of providing the network good

n :

Size of small sub-network which coordinates to recruit a new adopter

r :

reward paid by seller to a network member recruiting a new adopter

u 0 :

Constant in the linear model of u(x): \(u(x) = u_0 - \lambda x\)

u(x):

Stand-alone utility (i.e., excluding network externalities) which consumer x derives from the good

u(y):

Utility that each adopter derives due to the network effect when the network size equals y

\(y_i^*\) :

Marginal adopter in equilibrium, in model i

α :

Slope parameter in the linear model of v(y): \(v(y) = \alpha y\)

κ :

Cost leveraging factor: When a user exerts peer influence on some not-yet-adopter, the resulting benefit for the wooed individual equals κ times the cost that the influencer incurs

λ :

Slope parameter in the linear model of u(x): \(u(x) = u_0 - \lambda x\)

ω :

\(\omega \equiv \alpha / \lambda \) measures the relative strength of the network externality

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Henkel, J., Block, J. Peer influence in network markets: a theoretical and empirical analysis. J Evol Econ 23, 925–953 (2013). https://doi.org/10.1007/s00191-012-0302-4

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