Econometric Inference on Large Bayesian Games with Heterogeneous Beliefs

Econometric models of strategic interactions among people or firms have received a great deal of attention in the literature. Less attention has been paid to the role of the underlying assumptions about the way agents form beliefs about other agents. This paper focuses on a single large Bayesian game and develops a bootstrap inference method that relaxes the assumption of rational expectations and allows for the players to form beliefs differently from each other. By drawing on the main intuition of Kalai(2004), we introduce the notion of a hindsight regret, which measures each player's ex post value of other players' type information, and obtain its belief-free bound. Using this bound, we derive testable implications and develop a bootstrap inference procedure for the structural parameters. We demonstrate the finite sample performance of the method through Monte Carlo simulations.