Endogeneity in Discrete Bayesian Games: U.S. Cellphone Service Deployment

Abstract

In some Bayesian games, payoff-relevant states are influenced by unobserved player- or game-level heterogeneity that also also effects strategic decisions directly. Ignoring such endogeneity in empirical analysis leads to erroneous inference of structural parameters and policy implications. We introduce a control-function approach for estimating discrete Bayesian games with such endogeneity. We apply the method to analyze an entry game of deploying 4G-LTE technology by major U.S. cellphone service providers, taking existing network deployment in the focal market and current deployment in neighboring markets as endogenous. Using lagged demographics of neighboring markets as instruments, we find that a hypothetical T-Mobile and Sprint merger would reduce 4G-LTE deployment across local markets. Moreover, the entry of a fourth national provider, enabled by a partial divestiture of the merger’s assets, would not completely offset its negative impact on market entries and the population served. We also find that ignoring endogeneity in network deployment skews the policy implications by underpredicting the merger’s negative impacts on market entry.