Minimax Regret and Strategic Uncertainty

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)).

[1]  E. Damme.  Refinements of the Nash Equilibrium Concept , 1983 .

[2]  Zvika Neeman,et al.  Common Beliefs and the Existence of Speculative Trade , 1996 .

[3]  Leonard J. Savage,et al.  The Theory of Statistical Decision , 1951 .

[4]  Adam Brandenburger,et al.  Rationalizability and Correlated Equilibria , 1987 .

[5]  A. Tversky,et al.  Choice in Context: Tradeoff Contrast and Extremeness Aversion , 1992 .

[6]  Craig Boutilier,et al.  Regret Minimizing Equilibria and Mechanisms for Games with Strict Type Uncertainty , 2004, UAI.

[7]  Joseph Y. Halpern,et al.  Iterated Regret Minimization: A More Realistic Solution Concept , 2008, ArXiv.

[8]  Colin Camerer.  Behavioral Game Theory , 1990 .

[9]  D. Bergemann,et al.  Robust Monopoly Pricing: The Case of Regret , 2005 .

[10]  E. Fehr.  A Theory of Fairness, Competition and Cooperation , 1998 .

[11]  Takashi Hayashi.  Dynamic choice with anticipated regret , 2008 .

[12]  B. Bernheim.  Rationalizable Strategic Behavior , 1984 .

[13]  S. Morris.  The Common Prior Assumption in Economic Theory , 1995, Economics and Philosophy.

[14]  R. Aumann,et al.  Epistemic Conditions for Nash Equilibrium , 1995 .

[15]  Kin Chung Lo,et al.  Equilibrium in Beliefs under Uncertainty , 1996 .

[16]  Sujoy Mukerji,et al.  A theory of play for games in strategic form when rationality is not common knowledge , 1995 .

[17]  Takashi Hayashi,et al.  Regret aversion and opportunity dependence , 2008, J. Econ. Theory.

[18]  Stephen Morris,et al.  Ex Post Implementation , 2005, Games Econ. Behav..

[19]  P. Reny.  On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games , 1999 .

[20]  Peter Klibanofi,et al.  Uncertainty, Decision, and Normal Form Games , 1996 .

[21]  Clemens Puppe,et al.  Choice under complete uncertainty when outcome spaces are state dependent , 2009 .

[22]  Peter B. Linhart.  Bargaining solutions with non-standard objectives , 2001 .

[23]  F. J. Anscombe,et al.  A Definition of Subjective Probability , 1963 .

[24]  E. Vandamme.  Stability and perfection of nash equilibria , 1987 .

[25]  Roy Radner,et al.  Minimax-regret strategies for bargaining over several variables , 1989 .

[26]  Oriol Carbonell-Nicolau.  Games and Economic Behavior , 2011 .

[27]  J. Milnor.  Games Against Nature , 1951 .

[28]  Michael R. Baye,et al.  Price Dispersion in the Lab and on the Internet: Theory and Evidence , 2004 .

[29]  Jörg Stoye,et al.  Axioms for minimax regret choice correspondences , 2011, J. Econ. Theory.

[30]  Jörg Stoye,et al.  Statistical decisions under ambiguity , 2011 .

[31]  M. Rabin,et al.  Understanding Social Preference with Simple Tests , 2001 .

[32]  D. Bergemann,et al.  Pricing Without Priors , 2007 .

[33]  D. Fudenberg,et al.  Self-confirming equilibrium , 1993 .

[34]  Ludovic Renou,et al.  Homo Sapiens Sapiens Meets Homo Strategicus at the Laboratory , 2008 .

[35]  Ludovic Renou,et al.  Minimax Regret and Strategic Uncertainty , 2008 .

[36]  David Pearce.  Rationalizable Strategic Behavior and the Problem of Perfection , 1984 .

[37]  Dirk Bergemann,et al.  Robust Monopoly Pricing , 2008, J. Econ. Theory.

[38]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[39]  Peter B. Linhart.  original papers : Bargaining solutions with non-standard objectives , 2001 .

[40]  Massimo Marinacci,et al.  Ambiguous Games , 2000, Games Econ. Behav..