Evolution of theories of mind

This paper studies the evolution of peoplesʼ models of how other people think – their theories of mind. This is formalized within the level-k model, which postulates a hierarchy of types, such that type k plays a k times iterated best response to the uniform distribution. It is found that, under plausible conditions, lower types co-exist with higher types. The results are extended to a model of learning, in which type k plays a k times iterated best response the average of past play. The model is also extended to allow for partial observability of the opponentʼs type.

[1]  Johan Stennek.  The survival value of assuming others to be rational , 2000, Int. J. Game Theory.

[2]  X. Vives.  Nash equilibrium with strategic complementarities , 1990 .

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

[4]  Toshiji Kawagoe,et al.  Equilibrium refinement vs. level-k analysis: An experimental study of cheap-talk games with private information , 2009, Games Econ. Behav..

[5]  A. Jolly,et al.  Lemur Social Behavior and Primate Intelligence , 1966, Science.

[6]  William H. Sandholm,et al.  Potential Games with Continuous Player Sets , 2001, J. Econ. Theory.

[7]  Takatoshi Ito,et al.  A Filippov solution of a system of differential equations with discontinuous right-hand sides , 1979 .

[8]  Dale O. Stahl,et al.  Evolution of Smartn Players , 1993 .

[9]  D. Sgroi,et al.  Learning to play 3×3 games: Neural networks as bounded-rational players , 2009 .

[10]  Jeffrey C. Ely,et al.  Evolution of Preferences1 , 2007 .

[11]  Robin I. M. Dunbar.  The Social Brain: Mind, Language, and Society in Evolutionary Perspective , 2003 .

[12]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[13]  Carol V. Ward,et al.  Ecological dominance, social competition, and coalitionary arms races: Why humans evolved extraordinary intelligence. , 2005 .

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

[15]  F. A. Hayek.  The American Economic Review , 2007 .

[16]  Robin I. M. Dunbar.  Social Brain Hypothesis , 1998, Encyclopedia of Evolutionary Psychological Science.

[17]  Jakub Steiner,et al.  Contagion through learning , 2008 .

[18]  L. Samuelson,et al.  Evolutionary Stability in Asymmetric Games , 1992 .

[19]  Jens Josephson,et al.  A numerical analysis of the evolutionary stability of learning rules , 2008 .

[20]  Josef Hofbauer,et al.  The theory of evolution and dynamical systems , 1988 .

[21]  Jeffrey C. Ely,et al.  Evolution of Preferences -super-1 , 2007 .

[22]  M. Friedman.  Essays in Positive Economics , 1954 .

[23]  R. Nagel,et al.  Neural correlates of depth of strategic reasoning in medial prefrontal cortex , 2009, Proceedings of the National Academy of Sciences.

[24]  O. Volij,et al.  Field Centipedes , 2006 .

[25]  Franz J. Weissing,et al.  Evolutionary stability and dynamic stability in a class of evolutionary normal form games , 1991 .

[26]  Robert Östling,et al.  When Does Communication Improve Coordination , 2010 .

[27]  Kaushik Basu,et al.  The traveler's dilemma: Paradoxes of rationality in game theory , 1994 .

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

[29]  S. Gould,et al.  Evolution of the brain and intelligence. , 1974, Science.

[30]  Dana Heller,et al.  An evolutionary approach to learning in a changing environment , 2004, J. Econ. Theory.

[31]  L. Shapley,et al.  REGULAR ARTICLEPotential Games , 1996 .

[32]  Amnon Rapoport,et al.  Depth of reasoning in strategic form games , 2006 .

[33]  P. Tobias.  Evolution of the Human Brain , 2000 .

[34]  M. Tomasello,et al.  Does the chimpanzee have a theory of mind? 30 years later , 2008, Trends in Cognitive Sciences.

[35]  Dorothea Kübler,et al.  Limited Depth of Reasoning and Failure of Cascade Formation in the Laboratory , 2001 .

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

[37]  N. Humphrey.  The Social Function of Intellect , 1976 .

[38]  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 .

[39]  Friederike Mengel,et al.  Learning across games , 2012, Games Econ. Behav..

[40]  D. Fudenberg,et al.  The Theory of Learning in Games , 1998 .

[41]  G. Roth,et al.  Evolution of the brain and intelligence , 2005, Trends in Cognitive Sciences.

[42]  Toshiji Kawagoe,et al.  Equilibrium refinement vs. level-k analysis: An experimental study of cheap-talk games with private information , 2009 .

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

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

[45]  L. Cosmides,et al.  Cognitive adaptations for social exchange. , 1992 .

[46]  Jeffrey C. Ely,et al.  Evolution of Preferences , 2007 .

[47]  D. Stahl.  Evolution of Smart n Players , 1991 .

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

[49]  H. Young,et al.  The Evolution of Conventions , 1993 .

[50]  J. Bert,et al.  Evolution of the Human Brain , 1972, Nature.

[51]  L. Cosmides,et al.  The Adapted mind : evolutionary psychology and the generation of culture , 1992 .

[52]  L. Shapley.  SOME TOPICS IN TWO-PERSON GAMES , 1963 .

[53]  William H. Sandholm,et al.  Population Games And Evolutionary Dynamics , 2010, Economic learning and social evolution.

[54]  Dale O. Stahl,et al.  Rule Learning in Symmetric Normal-Form Games: Theory and Evidence , 2000, Games Econ. Behav..

[55]  R. Nagel.  Unraveling in Guessing Games: An Experimental Study , 1995 .

[56]  R. Byrne,et al.  Machiavellian intelligence : social expertise and the evolution of intellect in monkeys, apes, and humans , 1990 .

[57]  Drew Fudenberg,et al.  Heterogeneous beliefs and local information in stochastic fictitious play , 2011, Games Econ. Behav..

[58]  Dale O. Stahl,et al.  Evidence based rules and learning in symmetric normal-form games , 1999, Int. J. Game Theory.

[59]  Jaap J. A. Denissen,et al.  The evolutionary genetics of personality , 2007 .

[60]  Larry Samuelson,et al.  Introduction to the Evolution of Preferences , 2001, J. Econ. Theory.

[61]  Miguel A. Costa-Gomes,et al.  Cognition and Behavior in Normal-Form Games: An Experimental Study , 1998 .

[62]  Richard D. Alexander,et al.  How did humans evolve? Reflections on the uniquely unique species. , 1990 .

[63]  Eswar S. Prasad,et al.  Forthcoming in the American Economic Review , 2006 .

[64]  Arthur J. Robson,et al.  The evolution of rationality and the Red Queen , 2003, J. Econ. Theory.

[65]  William H. Sandholm,et al.  The projection dynamic and the geometry of population games , 2008, Games Econ. Behav..

[66]  Dale O. Stahl,et al.  Learning Transference Between Dissimilar Symmetric Normal-Form Games , 2008 .

[67]  Ian A. Apperly,et al.  The cost of thinking about false beliefs: Evidence from adults’ performance on a non-inferential theory of mind task , 2008, Cognition.

[68]  A. Alchian.  Uncertainty, Evolution, and Economic Theory , 1950, Journal of Political Economy.

[69]  Reinhard Selten,et al.  Game equilibrium models , 1991 .

[70]  Larry Samuelson,et al.  Analogies, Adaptation, and Anomalies , 2001, J. Econ. Theory.

[71]  D. Dennett.  The Intentional Stance. , 1987 .

[72]  D. Premack,et al.  Does the chimpanzee have a theory of mind? , 1978, Behavioral and Brain Sciences.

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

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

[75]  V. Crawford.  Lying for Strategic Advantage: Rational and Boundedly Rational Misrepresentation of Intentions , 2003 .

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

[77]  Robin I. M. Dunbar,et al.  Theory-of-mind deficits and causal attributions , 1998 .

[78]  Jörgen W. Weibull,et al.  Evolutionary Game Theory , 1996 .