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

Abstract

I study identification 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, payoffs are identified. All the equilibria of the model are also then identified. As \textit{payoff 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 satisfied, payoffs, equilibria and the distribution of the payoff relevant unobservable are identified. Additionally, letting $A$ be the number of choice alternatives, $N$ the number of players and $K$ the number of equilibria, as long as $A^N\geq K$, I show that equilibrium selection probabilities are also identified, a result that is useful for considering the effects of counterfactual experiments in the presence of multiple equilibria. I extend the framework to study identification in dynamic games. The static approach extends in a straightforward way to finite horizon (non-stationary) games, but not to the more common case of infinite horizon (stationary) games. I show that by making additional testable restrictions on the transition probabilities, a large class of stationary dynamic games are also identified.