Empirical Framework for Two-Player Repeated Games with Random States

We provide methods for the empirical analysis of a class of two-player repeated games with i.i.d. shocks, allowing for non-Markovian strategies. The number of possible equilibria in these games is large and, usually, theory is silent about which equilibrium will be chosen in practice. Thus, our method remains agnostic about selection among these multiple equilibria, which leads to partial identification of the parameters of the game. We propose a profiled likelihood criterion for building confidence sets for the structural parameters of the game and derive an easily computable upper bound on the critical value. We demonstrate good finite-sample performance of our procedure using a simulation study. We illustrate the usefulness of our method by studying the effect of repealing the Wright Amendment on entry and exit into Dallas airline markets and find that the static game approach overestimates the negative effect of the law on entry into these markets.