Testing Equilibrium Multiplicity in Dynamic Games

This paper proposes several statistical tests for finite state Markov games to examine the null hypothesis that the data are generated from a single equilibrium. We formulate tests of (i) the conditional choice and state transition probabilities, (ii) the steady-state distribution, and (iii) the conditional state distribution given an initial state. In a Monte Carlo study we find that the test based on the steady-state distribution performs well and has high power even with small numbers of markets and time periods. We apply the tests to the empirical study of Ryan (2012) that analyzes dynamics of the U.S. Portland Cement industry and assess if his assumption of single equilibrium is supported by the data.