Heterogeneous quantal response equilibrium and cognitive hierarchies

We explore an equilibrium model of games where behavior is given by logit response functions, but payoff responsiveness and beliefs about others' responsiveness are heterogeneous. We study two substantively different ways of extending quantal response equilibrium (QRE) to this setting: (1) Heterogeneus QRE, where players share identical correct beliefs about the distribution of payoff responsiveness; and (2) Truncated QRE, where players have downward looking beliefs, systematically underestimating others' responsiveness. We show that the cognitive hierarchy model is a special case of Truncated QRE. We conduct experiments designed to differentiate these approaches. We find significant evidence of payoff responsive stochastic choice, and of heterogeneity and downward looking beliefs in some games.

[1]  D. Stahl,et al.  On Players' Models of Other Players: Theory and Experimental Evidence , 1995 .

[2]  Charles A. Holt,et al.  Anomalous Behavior in a Traveler's Dilemma? , 1999 .

[3]  Miguel A. Costa-Gomes,et al.  Cognition and Behavior in Two-Person Guessing Games: An Experimental Study , 2003 .

[4]  R. McKelvey,et al.  Quantal Response Equilibria for Extensive Form Games , 1998 .

[5]  Eric J. Johnson,et al.  Detecting Failures of Backward Induction: Monitoring Information Search in Sequential Bargaining , 2002, J. Econ. Theory.

[6]  A. Tversky,et al.  On the psychology of prediction , 1973 .

[7]  T. Palfrey,et al.  Risk Averse Behavior in Asymmetric Matching Pennies Games , 2000 .

[8]  R. McKelvey,et al.  An experimental study of the centipede game , 1992 .

[9]  V. Crawford,et al.  Level-k Auctions: Can a Non-Equilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions? , 2007 .

[10]  D. Monderer,et al.  On Rationality, Learning and Zero-Sum Betting - An Experimental Study of the No-Betting Conjecture , 2001 .

[11]  Drew Fudenberg,et al.  The Folk Theorem in Repeated Games with Discounting or with Incomplete Information , 1986 .

[12]  T. Scharping.  Hide-and-seek: China's elusive population data , 2001 .

[13]  Joel Sobel,et al.  A Model of Positive Self-Image in Subjective Assessments , 2005 .

[14]  Nancy L. Stokey,et al.  Information, Trade, and Common Knowledge , 1982 .

[15]  David M. Kreps,et al.  Rational cooperation in the finitely repeated prisoners' dilemma , 1982 .

[16]  S. Gächter.  Behavioral Game Theory , 2008, Encyclopedia of Evolutionary Psychological Science.

[17]  R. McKelvey,et al.  An experimental study of constant-sum centipede games , 1996 .

[18]  Robert J. Weber,et al.  Distributional Strategies for Games with Incomplete Information , 1985, Math. Oper. Res..

[19]  Colin Camerer,et al.  A cognitive hierarchy theory of one-shot games: Some preliminary results , 2003 .

[20]  Eric Maskin,et al.  The Existence of Equilibrium with Price-Setting Firms , 1986 .

[21]  Georg Weizsäcker.  Ignoring the Rationality of Others: Evidence from Experimental Normal-form Games , 2001 .

[22]  Jacob K. Goeree,et al.  Risk averse behavior in generalized matching pennies games , 2003, Games Econ. Behav..

[23]  Roberto A. Weber,et al.  The effects of payoff magnitude and heterogeneity on behavior in 2 x 2 games with unique mixed strategy equilibria , 2000 .

[24]  R. Duncan Luce,et al.  Individual Choice Behavior , 1959 .

[25]  J. Harsanyi.  Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points , 1973 .

[26]  I. Glicksberg.  A FURTHER GENERALIZATION OF THE KAKUTANI FIXED POINT THEOREM, WITH APPLICATION TO NASH EQUILIBRIUM POINTS , 1952 .

[27]  Charles A. Holt,et al.  Ten Little Treasures of Game Theory and Ten Intuitive Contradictions , 2001 .

[28]  Ylva Søvik.  Strength of dominance and depths of reasoning—An experimental study , 2009 .

[29]  Jacob K. Goeree,et al.  A model of noisy introspection , 2004, Games Econ. Behav..

[30]  T. Palfrey,et al.  The Compromise Game: Two-Sided Adverse Selection in the Laboratory , 2007 .

[31]  Dan Lovallo,et al.  To Review or Not to Review? Limited Strategic Thinking at the Movie Box Office , 2009 .

[32]  John Morgan,et al.  An Experimental Investigation of Unprofitable Games , 2002, Games Econ. Behav..

[33]  R. Aumann,et al.  Unraveling in Guessing Games : An Experimental Study , 2007 .

[34]  Arumugam Rajesh.  To Review or Not to Review , 2011 .

[35]  Charles A. Holt,et al.  Regular Quantal Response Equilibrium , 2005 .

[36]  Thomas R. Palfrey,et al.  A Bayesian Sequential Experimental Study of Learning in Games , 1993 .

[37]  Colin Camerer,et al.  Overconfidence and Excess Entry: An Experimental Approach , 1999 .

[38]  J. Ochs.  Games with Unique, Mixed Strategy Equilibria: An Experimental Study , 1995 .

[39]  B. O'Neill.  Nonmetric test of the minimax theory of two-person zerosum games. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[40]  Colin Camerer,et al.  Sophisticated EWA Learning and Strategic Teaching in Repeated Games , 2000 .

[41]  Colin Camerer,et al.  A Cognitive Hierarchy Model of Games , 2004 .

[42]  V. Crawford,et al.  Fatal Attraction: Focality, Naivete, and Sophistication in Experimental "Hide-and-Seek" Games , 2007 .

[43]  Colin Camerer,et al.  Field and Lab Convergence in Poisson LUPI Games , 2007 .

[44]  R. McKelvey,et al.  Quantal Response Equilibria for Normal Form Games , 1995 .