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

Alfred Galichon

NYU, Department of Economics and Courant Institute

Marc Henry

Pennsylvania State University

Date Written: February 15, 2011

Abstract

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

Galichon, Alfred and Henry, Marc, Set Identification in Models with Multiple Equilibria (February 15, 2011). Review of Economic Studies, Vol. 78, No. 4, pp. 1264-1298, 2011. Available at SSRN: https://ssrn.com/abstract=1134762

Alfred Galichon (Contact Author)

NYU, Department of Economics and Courant Institute ( email )

269 Mercer Street, 7th Floor
New York, NY 10011
United States

Marc Henry

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

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