Econometric Inference on a Large Bayesian Game with Heterogeneous Beliefs

TL;DR

This paper develops an econometric approach for large Bayesian games that relaxes rational expectations, introduces hindsight regret for belief modeling, and provides a robust inference method with strong finite sample performance.

Contribution

It introduces a belief-free inference framework for large Bayesian games using hindsight regret, accommodating heterogeneous beliefs and large strategic neighborhoods.

Findings

Inference method is valid regardless of neighborhood size

Method exhibits high power with large neighborhoods

Finite sample performance demonstrated via simulations

Abstract

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. We focus on a single large Bayesian game with idiosyncratic strategic neighborhoods and develop an approach of empirical modeling that relaxes the assumption of rational expectations and allows the players to form beliefs differently. By drawing on the main intuition of Kalai (2004), we introduce the notion of hindsight regret, which measures each player's ex-post value of other players' type information, and obtain the belief-free bound for the hindsight regret. Using this bound, we derive testable implications and develop a bootstrap inference procedure for the structural parameters. Our inference method is uniformly valid regardless of the size of strategic neighborhoods and tends to exhibit high power when the neighborhoods are large. We demonstrate the finite sample performance of the method through Monte Carlo simulations.