Learning across games

This paper studies the learning process carried out by two agents who are involved in many games. As distinguishing all games can be too costly (require too much reasoning resources) agents might partition the set of all games into categories. Partitions of higher cardinality are more costly. A process of simultaneous learning of actions and partitions is presented and equilibrium partitions and action choices characterized. Learning across games can destabilize strict Nash equilibria even for arbitrarily small reasoning costs and even if players distinguish all the games at the stable point. The model is also able to explain experimental findings from the travelerʼs dilemma and deviations from subgame perfection in bargaining games.

[1]  A. Rubinstein Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?) , 1988 .

[2]  Pierre Priouret,et al.  Adaptive Algorithms and Stochastic Approximations , 1990, Applications of Mathematics.

[3]  Philippe Jehiel,et al.  Analogy-based expectation equilibrium , 2004, J. Econ. Theory.

[4]  Drew Fudenberg,et al.  Learning Purified Mixed Equilibria , 2000, J. Econ. Theory.

[5]  Jakub Steiner,et al.  Learning by Similarity in Coordination Problems , 2007 .

[6]  Friederike Mengel,et al.  Matching structure and the cultural transmission of social norms , 2008 .

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

[8]  M. Cripps The theory of learning in games. , 1999 .

[9]  E. Hopkins Two Competing Models of How People Learn in Games (first version) , 1999 .

[10]  V. Grimm,et al.  GROUP SELECTION WITH IMPERFECT SEPARATION - AN EXPERIMENT , 2007 .

[11]  Veronika Grimm,et al.  An experiment on learning in a multiple games environment , 2012, J. Econ. Theory.

[12]  A. Roth,et al.  Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria , 1998 .

[13]  H. Young Individual Strategy and Social Structure , 2020 .

[14]  F. Mengel,et al.  Investment Incentives in Auctions: An Experiment , 2006 .

[15]  Dov Samet,et al.  Learning to play games in extensive form by valuation , 2001, J. Econ. Theory.

[16]  Kfir Eliaz,et al.  Nash equilibrium when players account for the complexity of their forecasts , 2003, Games Econ. Behav..

[17]  M. Bacharach Economics and the Theory of Games , 2019 .

[18]  F. Germano Stochastic Evolution of Rules for Playing Finite Normal Form Games , 2007 .

[19]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[20]  R. Pemantle,et al.  Nonconvergence to Unstable Points in Urn Models and Stochastic Approximations , 1990 .

[21]  Ran Spiegler Simplicity of beliefs and delay tactics in a concession game , 2004, Games Econ. Behav..

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

[23]  E. Kalai,et al.  Subjective Games and Equilibria , 1993 .

[24]  A. Rubinstein Modeling Bounded Rationality , 1998 .

[25]  I. Gilboa,et al.  Case-Based Decision Theory , 1995 .

[26]  Philip A. Haile,et al.  On the Empirical Content of Quantal Response Equilibrium , 2003 .

[27]  William H. Sandholm,et al.  ON THE GLOBAL CONVERGENCE OF STOCHASTIC FICTITIOUS PLAY , 2002 .

[28]  A. Roth,et al.  Learning in Extensive-Form Games: Experimental Data and Simple Dynamic Models in the Intermediate Term* , 1995 .

[29]  Itzhak Gilboa,et al.  Case-Based Optimization , 1996 .

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

[31]  L. Blume The Statistical Mechanics of Strategic Interaction , 1993 .

[32]  Marco LiCalzi Fictitious Play by Cases , 1995 .

[33]  N. Rescher,et al.  Essays in Honor of Carl G. Hempel , 1969 .

[34]  Dan Schuch,et al.  The research assistant , 2001 .

[35]  R. Selten,et al.  Alternating bid bargaining with a smallest money unit , 2005 .

[36]  M. Hirsch,et al.  Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games , 1999 .

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

[38]  Debraj Ray,et al.  Evolving Aspirations and Cooperation , 1998 .

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

[40]  Arthur J. Robson,et al.  Why Would Nature Give Individuals Utility Functions? , 2001, Journal of Political Economy.

[41]  Martin Posch,et al.  Cycling in a stochastic learning algorithm for normal form games , 1997 .

[42]  M. Benaïm,et al.  Deterministic Approximation of Stochastic Evolution in Games , 2003 .

[43]  Tilman Börgers,et al.  Naive Reinforcement Learning With Endogenous Aspirations , 2000 .

[44]  A. Ianni,et al.  Reinforcement learning and the power law of practice: some analytical results , 2002 .

[45]  R. Luce Semiorders and a Theory of Utility Discrimination , 1956 .

[46]  Alexander Bird,et al.  Natural Kinds , 1988, Philosophy.

[47]  F. Mengel The evolution of function-valued traits for conditional cooperation. , 2007, Journal of theoretical biology.

[48]  A. Rubinstein,et al.  The Structure of Nash Equilibrium in Repeated Games with Finite Automata (Now published in Econometrica, 56 (1988), pp.1259-1282.) , 1986 .

[49]  H. Kushner,et al.  Stochastic Approximation and Recursive Algorithms and Applications , 2003 .

[50]  Jean-François Laslier,et al.  A Behavioral Learning Process in Games , 2001, Games Econ. Behav..

[51]  Josef Hofbauer,et al.  Learning in perturbed asymmetric games , 2005, Games Econ. Behav..

[52]  E. Hopkins Adaptive learning models of consumer behavior , 2007 .

[53]  Josef Hofbauer,et al.  Evolution in games with randomly disturbed payoffs , 2007, J. Econ. Theory.

[54]  Axel Ockenfels,et al.  An Evolutionary Analysis of Buyer Insurance and Seller Reputation in Online Markets , 2007 .

[55]  Josep M. Porta,et al.  Reinforcement-based learning with automatic categorization , 1999 .

[56]  Tilman Börgers,et al.  Learning Through Reinforcement and Replicator Dynamics , 1997 .

[57]  Ken Binmore,et al.  A Backward Induction Experiment , 2002, J. Econ. Theory.

[58]  Eric B. Baum,et al.  What is thought? , 2003 .

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