Set Identification in Models with Multiple Equilibria
Review of Economic Studies, Vol. 78, No. 4, pp. 1264-1298, 2011
46 Pages Posted: 20 May 2008 Last revised: 4 Nov 2011
Date Written: February 15, 2011
We propose a computationally feasible way of deriving the identified features of models with multiple equilibria in pure or mixed strategies. It is shown that in the case of Shapley regular normal form games, the identified set is characterized by the inclusion of the true data distribution within the core of a Choquet capacity, which is interpreted as the generalized likelihood of the model. In turn, this inclusion is characterized by a finite set of inequalities and efficient and easily implementable combinatorial methods are described to check them. In all normal form games, the identified set is characterized in terms of the value of a submodular or convex optimization program. Efficient algorithms are then given and compared to check inclusion of a parameter in this identified set. The latter are illustrated with family bargaining games and oligopoly entry games.
Keywords: multiple equilibria, optimal transportation, identification regions, core determining classes
JEL Classification: C13, C72
Suggested Citation: Suggested Citation