Testing for Monotone Equilibrium Strategies in Games of Incomplete Information

TL;DR

This paper introduces a new statistical testing framework for verifying monotone Bayesian Nash equilibrium strategies in incomplete information games, applicable with covariates and heterogeneity.

Contribution

It reformulates the monotonicity testing problem as moment inequalities and proposes a bootstrap-based Cramer-von Mises test for practical implementation.

Findings

The method accurately detects monotonic strategies in simulations.

It effectively incorporates covariates and heterogeneity.

Application to auctions demonstrates cartel detection capability.

Abstract

This paper develops a unified framework for testing monotonicity of Bayesian Nash equilibrium strategies in unobserved types in games of incomplete information. We show that, under symmetric independent private types, monotonicity of differentiable equilibrium strategies is equivalent to monotonicity of a quasi-inverse strategy identified from observed actions. This allows the problem to be reformulated as testing a countable set of moment inequalities involving unconditional expectations. We propose a Cramer-von Mises-type statistic with bootstrap critical values. The method accommodates covariates and game heterogeneity. Monte Carlo simulations demonstrate finite-sample performance, and an application to procurement auctions illustrates cartel detection.