Endogeneity in Games with Incomplete Information: U.S. Cellphone Service Deployment

Abstract

In some discrete games with incomplete information, payoff-relevant states are influenced by unobserved heterogeneity that also directly affects strategic decisions. When ignored, such endogeneity potentially leads to problematic parameter inference and policy implications. We introduce a control-function (CF) approach for estimating such games, and apply the method to an entry game of deploying 4G-LTE technology between major U.S. cellphone service providers. Unlike CF methods in single-agent contexts, our CF approach in the context of Bayesian
games is based on new conditions on how unobserved market and player heterogeneity correlate with sources of endogeneity and instruments. Taking network investment as endogenous, we find that a hypothetical T-Mobile and Sprint merger would reduce 4G-LTE deployment across the local markets in our sample, and disproportionately decrease rural coverage. Ignoring such endogeneity would under-predict the negative impacts of the merger, therefore favoring its approval.

Keywords: Endogeneity, Discrete Games with Incomplete Information, Control Function, Two-Step Nested Pseudo Likelihood, Entry Game, U.S. Cellphone Service

JEL Classification: C31, C35, C57, L13, L96