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Minimax regret and strategic uncertainty

  • Ludovic Renou
  • Karl Schlag

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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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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  1. Dirk Bergemann & Karl Schlag, 2005. "Robust Monopoly Pricing: The Case of Regret," Economics Working Papers ECO2005/10, European University Institute.
  2. Charness, Gary & Rabin, Matthew, 2001. "Understanding Social Preferences with Simple Tests," Department of Economics, Working Paper Series qt4qz9k8vg, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  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. Dirk Bergemann & Stephen Morris, 2006. "Ex Post Implementation," Levine's Bibliography 122247000000001110, UCLA Department of Economics.
  5. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  6. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57 World Scientific Publishing Co. Pte. Ltd..
  7. 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.
  8. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136 World Scientific Publishing Co. Pte. Ltd..
  9. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
  10. 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.
  11. Itzhak Gilboa & David Schmeidler, 1989. "Maxmin Expected Utility with Non-Unique Prior," Post-Print hal-00753237, HAL.
  12. Kin Chung Lo, 1995. "Equilibrium in Beliefs Under Uncertainty," Working Papers ecpap-95-02, University of Toronto, Department of Economics.
  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. 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.
  15. Drew Fudenberg & David K. Levine, 1993. "Self-Confirming Equilibrium," Levine's Working Paper Archive 2147, David K. Levine.
  16. 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.
  17. 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.
  18. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
  19. Marinacci, Massimo, 2000. "Ambiguous Games," Games and Economic Behavior, Elsevier, vol. 31(2), pages 191-219, May.
  20. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
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