Identification and Estimation of a Discrete Game by Observing its Correlated Equilibria

This paper studies the problem of identifying and estimating the normal-form payoff parameters of a simultaneous, discrete game of complete information where the equilibrium concept employed is correlated equilibrium rather than Nash equilibrium. We show that once we extend the equilibrium concept from Nash equilibrium to the correlated equilibrium, the identification and estimation of game-theoretic econometric models become simpler, since this extension avoids the usual requirement of computing all equilibria of games. To deal with the presence of multiple equilibria, unlike most other work on empirical games, we make use of the moment inequality restrictions induced by the underlying game-theoretic econometric models without making equilibrium selection assumptions. The resulting identified features of the model are sets of parameters such that the choice probabilities predicted by the econometric model are consistent with the empirical choice probabilities estimated from the data. The importance sampling technique is used to reduce computational burden and overcome the non-smoothness problems. We also show that the model selection tests for moment inequality models can be used to test equilibrium concepts such as correlated equilibrium versus Nash equilibrium.