Journal Article

Set Identification in Models with Multiple Equilibria

Alfred Galichon and Marc Henry

in The Review of Economic Studies

Published on behalf of Review of Economic Studies Ltd

Volume 78, issue 4, pages 1264-1298
Published in print October 2011 | ISSN: 0034-6527
Published online April 2011 | e-ISSN: 1467-937X | DOI: http://dx.doi.org/10.1093/restud/rdr008
Set Identification in Models with Multiple Equilibria

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  • Econometric and Statistical Methods and Methodology: General
  • Game Theory and Bargaining Theory

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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 transport; Identified set; Core determining classes; C13; C72

Journal Article.  13779 words.  Illustrated.

Subjects: Econometric and Statistical Methods and Methodology: General ; Game Theory and Bargaining Theory

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