  The literature on dynamic discrete games often assumes that the conditional
choice probabilities and the state transition probabilities are homogeneous
across markets and over time. We refer to this as the "homogeneity assumption"
in dynamic discrete games. This assumption enables empirical studies to
estimate the game's structural parameters by pooling data from multiple markets
and from many time periods. In this paper, we propose a hypothesis test to
evaluate whether the homogeneity assumption holds in the data. Our hypothesis
test is the result of an approximate randomization test, implemented via a
Markov chain Monte Carlo (MCMC) algorithm. We show that our hypothesis test
becomes valid as the (user-defined) number of MCMC draws diverges, for any
fixed number of markets, time periods, and players. We apply our test to the
empirical study of the U.S.\ Portland cement industry in Ryan (2012).
