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Set identification in models with multiple equilibria

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  • Marc Henry

    (Départment de sciences économiques)

  • Alfred Galichon

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.

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File URL: http://spire.sciencespo.fr/hdl:/2441/5rkqqmvrn4tl22s9mc4ao8ocg/resources/review-of-economic-studies-2011-galichon-1264-98.pdf
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Bibliographic Info

Paper provided by Sciences Po in its series Sciences Po publications with number info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg.

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Date of creation: 2011
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Publication status: Published in Review of Economic Studies, 2011, vol. 78, pp.1264-1298
Handle: RePEc:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg

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  1. Jovanovic, Boyan, 1989. "Observable Implications of Models with Multiple Equilibria," Econometrica, Econometric Society, vol. 57(6), pages 1431-37, November.
  2. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  3. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, 07.
  4. Elie Tamer & Federico Ciliberto, 2004. "Market Structure and Multiple Equilibria in Airline Markets," Econometric Society 2004 North American Winter Meetings 517, Econometric Society.
  5. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 70(1), pages 147-165, January.
  6. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
  7. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
  8. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  9. Bresnahan, Timothy F & Reiss, Peter C, 1990. "Entry in Monopoly Markets," Review of Economic Studies, Wiley Blackwell, vol. 57(4), pages 531-53, October.
  10. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 147-165.
  11. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
  12. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09.
  13. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2008. "Sharp identification regions in games," CeMMAP working papers CWP15/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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Cited by:
  1. Coroneo, Laura & Corradi, Valentina & Santos Monteiro, Paulo, 2012. "Testing for optimal monetary policy via moment inequalities," The Warwick Economics Research Paper Series (TWERPS) 985, University of Warwick, Department of Economics.
  2. Galichon, Alfred & Henry, Marc, 2013. "Dilation bootstrap," Journal of Econometrics, Elsevier, vol. 177(1), pages 109-115.
  3. 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.
  4. Marc Henry & Ismael Mourifie, 2014. "Sharp Bounds in the Binary Roy Model," Working Papers tecipa-506, University of Toronto, Department of Economics.
  5. Andrew Chesher & Adam Rosen, 2014. "Generalized instrumental variable models," CeMMAP working papers CWP04/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. 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.
  7. 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.
  8. Fan, Yanqin & Park, Sang Soo, 2010. "Confidence sets for some partially identified parameters," MPRA Paper 37149, University Library of Munich, Germany.
  9. 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.
  10. Aradillas-Lopez, Andres, 2012. "Pairwise-difference estimation of incomplete information games," Journal of Econometrics, Elsevier, vol. 168(1), pages 120-140.

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