Identi cation of Static and Dynamic Games of Incomplete Information with Multiple Equilibria in the Data

I study identi cation of games of incomplete information, both static and dynamic, when there are multiple equilibria in the data. In the case of static games, I show that if multiplicity disappears at a small subset of the support of the observables, payo s are identi ed. All the equilibria of the model are also then identi ed. As payo relevant unobservables are an alternative explanation to multiple equilibria for observed correlation in player actions conditional on observables, I allow for this type of variable and show that as long as a conditional exclusion restriction on the distribution of the unobservables is satis ed, payo s, equilibria and the distribution of the payo relevant unobservable are identi ed. Additionally, letting A be the number of choice alternatives, N the number of players and K the number of equilibria, as long as AN K, I show that equilibrium selection probabilities are also identi ed, a result that is useful for considering the e ects of counterfactual experiments in the presence of multiple equilibria. I extend the framework to study identi cation in dynamic games. The static approach extends in a straightforward way to nite horizon (non-stationary) games, but not to the more common case of in nite horizon (stationary) games. I show that by making additional testable restrictions on the transition probabilities, a large class of stationary dynamic games are also identi ed.