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Set Identification in Models with Multiple Equilibria

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  • Alfred Galichon
  • Marc Henry

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. Copyright 2011, Oxford University Press.

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Bibliographic Info

Article provided by Oxford University Press in its journal The Review of Economic Studies.

Volume (Year): 78 (2011)
Issue (Month): 4 ()
Pages: 1264-1298

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Handle: RePEc:oup:restud:v:78:y:2011:i:4:p:1264-1298

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Cited by:
  1. Federico Bugni & Ivan Canay & Xiaoxia Shi, 2014. "Inference for functions of partially identified parameters in moment inequality models," CeMMAP working papers CWP22/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Marc Henry & Romuald M�ango & Maurice Queyranne, 2012. "Combinatorial Bootstrap Inference IN in Prtially Identified Incomplete Structural Models," CIRJE F-Series CIRJE-F-837, CIRJE, Faculty of Economics, University of Tokyo.
  3. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2013. "Testing many moment inequalities," CeMMAP working papers CWP65/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Andrew Chesher & Adam Rosen, 2014. "Generalized instrumental variable models," CeMMAP working papers CWP04/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Jeremy T. Fox & Natalia Lazzati, 2012. "Identification of Potential Games and Demand Models for Bundles," NBER Working Papers 18155, National Bureau of Economic Research, Inc.
  6. Marc Henry & Ismael Mourifie, 2014. "Sharp Bounds in the Binary Roy Model," Working Papers tecipa-506, University of Toronto, Department of Economics.
  7. Aradillas-Lopez, Andres, 2012. "Pairwise-difference estimation of incomplete information games," Journal of Econometrics, Elsevier, vol. 168(1), pages 120-140.
  8. Galichon, Alfred & Henry, Marc, 2013. "Dilation bootstrap," Journal of Econometrics, Elsevier, vol. 177(1), pages 109-115.
  9. Fan, Yanqin & Park, Sang Soo, 2010. "Confidence sets for some partially identified parameters," MPRA Paper 37149, University Library of Munich, Germany.
  10. Laura Coroneo & Valentina Corradi & Paulo Santos Monteiro, 2013. "Testing for optimal monetary policy via moment inequalities," Discussion Papers 13/07, Department of Economics, University of York.

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