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Minimax regret and strategic uncertainty

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  • Renou, Ludovic
  • Schlag, Karl H.

Abstract

This paper introduces a new solution concept, a minimax regret equilibrium, which allows for the possibility that players are uncertain about the rationality and conjectures of their opponents. We provide several applications of our concept. In particular, we consider price-setting environments and show that optimal pricing policy follows a non-degenerate distribution. The induced price dispersion is consistent with experimental and empirical observations (Baye and Morgan (2004) [4]).

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 1 (January)
Pages: 264-286

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:1:p:264-286

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Minimax regret Rationality Conjectures Price dispersion Auction;

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References

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  1. Michael R. Baye & John Morgan, 2004. "Price Dispersion in the Lab and on the Internet: Theory and Evidence," RAND Journal of Economics, The RAND Corporation, vol. 35(3), pages 448-466, Autumn.
  2. Ludovic Renou & Ralph C. Bayer, 2008. "Homo Sapiens Sapiens Meets Homo Strategicus at the Laboratory," Discussion Papers in Economics 08/16, Department of Economics, University of Leicester, revised Nov 2008.
  3. Linhart, P. B. & Radner, R., 1989. "Minimax-regret strategies for bargaining over several variables," Journal of Economic Theory, Elsevier, vol. 48(1), pages 152-178, June.
  4. Dirk Bergemann & Karl Schlag, 2005. "Robust Monopoly Pricing," Cowles Foundation Discussion Papers 1527R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2007.
  5. Gary Charness & Matthew Rabin, 2002. "Understanding Social Preferences With Simple Tests," The Quarterly Journal of Economics, MIT Press, vol. 117(3), pages 817-869, August.
  6. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May.
  7. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
  8. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
  9. Dirk Bergemann & Stephen Morris, 2005. "Ex Post Implementation," Levine's Bibliography 784828000000000018, UCLA Department of Economics.
  10. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  11. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
  12. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July.
  13. Mukerji, S., 1995. "A theory of play for games in strategic form when rationality is not common knowledge," Discussion Paper Series In Economics And Econometrics 9519, Economics Division, School of Social Sciences, University of Southampton.
  14. Dirk Bergemann & Karl Schlag, 2005. "Robust Monopoly Pricing: The Case of Regret," Economics Working Papers ECO2005/10, European University Institute.
  15. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  16. Clemens Puppe & Karl Schlag, 2009. "Choice under complete uncertainty when outcome spaces are state dependent," Theory and Decision, Springer, vol. 66(1), pages 1-16, January.
  17. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
  18. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
  19. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
  20. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
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Citations

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Cited by:
  1. Dirk Bergemann & Karl Schlag, 2005. "Robust Monopoly Pricing," Cowles Foundation Discussion Papers 1527RR, Cowles Foundation for Research in Economics, Yale University, revised Sep 2008.
  2. Iverson, Terrence, 2013. "Minimax regret discounting," Journal of Environmental Economics and Management, Elsevier, vol. 66(3), pages 598-608.
  3. Ludovic Renou & Karl H. Schlag, 2009. "Implementation in Minimax Regret Equilibrium," Discussion Papers in Economics 09/24, Department of Economics, University of Leicester.
  4. Halpern, Joseph Y. & Pass, Rafael, 2012. "Iterated regret minimization: A new solution concept," Games and Economic Behavior, Elsevier, vol. 74(1), pages 184-207.
  5. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.

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