Discrete Games in Endogenous Networks: A Model of Network Effects on Consumer Choices.∗

This paper studies socioeconomic networks where agents make both decisions regarding network links and decisions regarding individual actions. In particular, I propose a behavioral model of network formation, where the network configuration arises as the cumulative outcome of agents’ optimal decisions over time rather than as the instantaneous outcome of a one-shot game with many players. Alternative protocols of network formation, sequential and k-coalition stage game, are discussed and it is shown that over time the network is absorbed in an equilibrium. Thus this paper contributes the discussion of how Nash (or in general any) equilibria come into being. Multiplicity of equilibria is a common problem in discrete games of complete information, which have been used to visualize a variety of contexts such as market entry, technology adoption, and peer effects. I develop an estimable specification of the framework, which allows me to deal with this problem in a novel way. In particular, the behavioral assumptions of the model naturally assign a probability to each equilibrium that can be used to form an integrated likelihood. I first discuss properties of a generic estimable specification of the model and then derive a closed-form expression for the likelihood. This presents an identification argument for model’s parameters and facilitates the estimation (say via Bayesian MCMC algorithm or simulated ML estimator). I use the likelihood to argue that this framework is robust to different techniques for capturing the strategic aspect of individuals’ behavior i.e. the sequential model of network dynamics is observationally equivalent to, what is termed as, (random k) k-player stage game dynamics. This is important in that it demonstrates that the model predictions do not hinge on ad hoc assumptions. In addition, the sequential framework is computationally easier to simulate and estimate with an appropriate data set. Finally, the link between the theoretical and the estimable model is discussed from the perspective of the notions of quantile response equilibrium and correlated equilibrium (McKelvey and Palfrey (1995), and Aumann (1974)). JEL Codes: D85, C73, L19