Testable Implications of Multiple Equilibria in Discrete Games with Correlated Types

TL;DR

This paper develops testable implications for multiple equilibria in discrete games with correlated private signals, extending previous work to include correlated types and dynamic settings, and demonstrates their practical implementation.

Contribution

It introduces new testable implications for multiple equilibria in static and dynamic discrete games with correlated private signals, expanding prior models.

Findings

Implications are applicable to static games with correlated private signals.

Dynamic games with serially correlated heterogeneity are analyzed using mixture distributions.

Existing statistical tools can implement these testable implications.

Abstract

We study testable implications of multiple equilibria in discrete games with incomplete information. Unlike de Paula and Tang (2012), we allow the players' private signals to be correlated. In static games, we leverage independence of private types across games whose equilibrium selection is correlated. In dynamic games with serially correlated discrete unobserved heterogeneity, our testable implication builds on the fact that the distribution of a sequence of choices and states are mixtures over equilibria and unobserved heterogeneity. The number of mixture components is a known function of the length of the sequence as well as the cardinality of equilibria and unobserved heterogeneity support. In both static and dynamic cases, these testable implications are implementable using existing statistical tools.