Ambiguous Act Equilibria

A game-theoretic framework that allows for explicitly randomized strategies is used to study the effect of ambiguity aversion on equilibrium outcomes. The notions of "independent strategies" as well as of "common priors" are amended to render them applicable to games in which players lack probabilistic sophistication. Within this framework the equilibrium predictions of two player games with ambiguity averse and with ambiguity neutral players are observationally equivalent. This equivalence result does not extend to the case of games with more than two players. A translation of the concept of equilibrium in beliefs to the context of ambiguity aversion yields substantially di erent predictions – even for the case with just two players.

[1]  Sérgio Ribeiro da Costa Werlang,et al.  Nash equilibrium under knightian uncertainty: breaking down backward induction (extensively revised version) , 1993 .

[2]  Burkhard C. Schipper,et al.  Ambiguity and Social Interaction , 2007 .

[3]  Colin Camerer,et al.  Recent developments in modeling preferences: Uncertainty and ambiguity , 1992 .

[4]  D. Schmeidler.  Subjective Probability and Expected Utility without Additivity , 1989 .

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

[6]  A. Rustichini,et al.  Ambiguity Aversion, Robustness, and the Variational Representation of Preferences , 2006 .

[7]  David Kelsey,et al.  Non-Additive Beliefs and Strategic Equilibria , 2000, Games Econ. Behav..

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

[9]  M. Marinacci,et al.  A Smooth Model of Decision Making Under Ambiguity , 2003 .

[10]  Dan Levin,et al.  Auctions with uncertain numbers of bidders , 2004, J. Econ. Theory.

[11]  Itzhak Gilboa,et al.  Uncertainty in economic theory : essays in honor of David Schmeidler's 65th birthday , 2004 .

[12]  David S. Ahn.  Ambiguity without a state space , 2004 .

[13]  Sujoy Mukerji,et al.  An overview of economic applications of David Schmeidler's models of decision making under uncertainty , 2004 .

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

[15]  Massimo Marinacci,et al.  Mutual absolute continuity of multiple priors , 2007, J. Econ. Theory.

[16]  Sophie Bade,et al.  Electoral Competition with Uncertainty Averse Parties , 2010 .

[17]  Larry G. Epstein.  Preference, Rationalizability and Equilibrium , 1997 .

[18]  Eddie Dekel,et al.  Lexicographic Probabilities and Choice Under Uncertainty , 1991 .

[19]  Sophie Bade.  Stochastic Independence with Maxmin Expected Utilities∗ , 2008 .

[20]  Roee Teper,et al.  Uncertainty Aversion and Equilibrium Existence in Games with Incomplete Information , 2009, Games Econ. Behav..

[21]  Peter Klibanoff,et al.  Stochastically independent randomization and uncertainty aversion , 2001 .

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

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

[24]  T. Bewley.  Knightian decision theory. Part I , 2002 .

[25]  Sophie Bade,et al.  Electoral Competition with Uncertainty Averse Parties , 2010, Games Econ. Behav..

[26]  J. Wooders,et al.  Minimax Play at Wimbledon , 2001 .

[27]  Massimo Marinacci,et al.  Uncertainty averse preferences , 2011, J. Econ. Theory.

[28]  Subir Bose,et al.  Optimal Auctions with Ambiguity , 2004 .

[29]  Refractor.  Uncertainty , 2001, The Lancet.

[30]  .. C. Hiappori,et al.  Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer , 2005 .

[31]  R. Aumann.  Subjectivity and Correlation in Randomized Strategies , 1974 .

[32]  Ehud Lehrer,et al.  Partially-Specified Probabilities: Decisions and Games , 2006 .

[33]  T. Sargent,et al.  Robust Control and Model Uncertainty , 2001 .

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

[35]  I. Gilboa,et al.  Sharing beliefs: between agreeing and disagreeing , 2000 .

[36]  Ignacio Palacios-Huerta.  Professionals Play Minimax , 2003 .