Testing for Monotone Equilibrium Strategies in Games of Incomplete Information
Yu-Chin Hsu, Tong Li, Chu-An Liu, Hidenori Takahashi
TLDR
A new statistical framework tests for monotone Bayesian Nash equilibrium strategies in incomplete information games, enabling detection of cartels in auctions.
Key contributions
- Develops a unified framework for testing monotonicity of Bayesian Nash equilibrium strategies.
- Reformulates the problem as testing moment inequalities using a quasi-inverse strategy.
- Proposes a Cramer-von Mises-type statistic with bootstrap critical values.
- Applies the method to procurement auctions for effective cartel detection.
Why it matters
This paper provides a robust statistical method to test fundamental assumptions about strategic behavior in complex economic models. Its practical application in detecting cartels in auctions offers a valuable tool for market regulation and anti-trust efforts.
Original 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.
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