Identification of Information Structures in Bayesian Games

Abstract

To what extent can an external observer infer the underlying information structure from an equilibrium action distribution in an incomplete-information game? We investigate this question in a general linear-quadratic-Gaussian framework. A simple class of canonical information structures is offered and proves rich enough to rationalize any equilibrium action distribution that can arise under an arbitrary information structure. Moreover, this class is parsimonious in the sense that its relevant parameters are uniquely identified from an observed equilibrium outcome. We then show that a canonical information structure characterizes the lower bound on the amount by which each agent's signal can reduce the state variance, across all observationally equivalent information structures. This identified lower bound can in turn be used to predict equilibrium action volatility following changes in the payoff structure.