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Minimax regret and strategic uncertainty

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  • Ludovic Renou
  • Karl Schlag

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 pricesetting 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)).

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Bibliographic Info

Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 1087.

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Date of creation: Apr 2008
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Handle: RePEc:upf:upfgen:1087

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Web page: http://www.econ.upf.edu/

Related research

Keywords: Minimax regret; rationality; conjectures; price dispersion; auction;

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References

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  1. Dirk Bergemann & Karl Schlag, 2005. "Robust Monopoly Pricing: The Case of Regret," Economics Working Papers, European University Institute ECO2005/10, European University Institute.
  2. Dirk Bergemann & Stephen Morris, 2005. "Ex Post Implementation," Cowles Foundation Discussion Papers 1502, Cowles Foundation for Research in Economics, Yale University.
  3. Dirk Bergemann & Karl Schlag, 2005. "Robust Monopoly Pricing," Cowles Foundation Discussion Papers 1527R, Cowles Foundation for Research in Economics, Yale University, revised Apr 2007.
  4. Drew Fudenberg & David K. Levine, 1993. "Self-Confirming Equilibrium," Levine's Working Paper Archive 2147, David K. Levine.
  5. Gary Charness & Matthew Rabin, 2002. "Understanding Social Preferences With Simple Tests," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 117(3), pages 817-869, August.
  6. Kin Chung Lo, 1995. "Equilibrium in Beliefs Under Uncertainty," Working Papers ecpap-95-02, University of Toronto, Department of Economics.
  7. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, Econometric Society, vol. 67(5), pages 1029-1056, September.
  8. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  9. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 63(5), pages 1161-80, September.
  10. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 55(6), pages 1391-1402, November.
  11. Michael R. Baye & John Morgan, 2004. "Price Dispersion in the Lab and on the Internet: Theory and Evidence," Working Papers, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy 2004-02, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
  12. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
  13. 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.
  14. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, Econometric Society, vol. 52(4), pages 1029-50, July.
  15. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
  16. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  17. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, Springer, vol. 70(2), pages 129-148, February.
  18. 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.
  19. Clemens Puppe & Karl Schlag, 2009. "Choice under complete uncertainty when outcome spaces are state dependent," Theory and Decision, Springer, Springer, vol. 66(1), pages 1-16, January.
  20. 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.
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Citations

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Cited by:
  1. Halpern, Joseph Y. & Pass, Rafael, 2012. "Iterated regret minimization: A new solution concept," Games and Economic Behavior, Elsevier, vol. 74(1), pages 184-207.
  2. Bergemann, Dirk & Schlag, Karl, 2011. "Robust monopoly pricing," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2527-2543.
  3. Renou, Ludovic & Schlag, Karl H., 2011. "Implementation in minimax regret equilibrium," Games and Economic Behavior, Elsevier, vol. 71(2), pages 527-533, March.
  4. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
  5. Iverson, Terrence, 2013. "Minimax regret discounting," Journal of Environmental Economics and Management, Elsevier, vol. 66(3), pages 598-608.

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