Correlated Equilibrium and the Estimation of Static Discrete Games with Complete Information

In order to understand strategic interactions among firms, we often need to estimate the parameters of static discrete games with complete information. This class of games is difficult to estimate because the possibility of multiple equilibria invalidates the use of methods such as MLE and GMM. We propose a two-step estimator to get around the issue of multiple equilibria by exploiting the fact that all of the Nash equilibria are contained in the set of correlated equilibria. In the first step, we estimate the conditional choice probabilities by which each possible outcome is realized. In the second step, we obtain the bounds on estimates of the parameters by minimizing the average distance between the set of correlated equilibria and the probability distribution that we obtained in the first step. Compared to previous approaches through which the issue of multiple equilibria has been tackled, our method has two important advantages. First, it explicitly takes into account the existence of mixed strategy equilibria. Second, it is computationally easy to implement: due to the inherent linearity of correlated equilibria, we can obtain the bounds estimates by solving a series of linear programming problems.