Learning with bounded memory in games

We study learning with bounded memory in zero-sum repeated games with one-sided incomplete information. The uninformed player has only a fixed number of memory states available. His strategy is to choose a transition rule from state to state, and an action rule, which is a map from each memory state to the set of actions. We show that the equilibrium transition rule involves randomization only in the intermediate memory states. Such randomization, or less frequent updating, is interpreted as a way of testing the opponent, which generates inertia in the player's behavior and is the main short-run bias in information processing exhibited by the bounded memory player.

[1]  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 .

[2]  M. Cripps,et al.  Imperfect Monitoring and Impermanent Reputations , 2002 .

[3]  N. Cowan.  The magical number 4 in short-term memory: A reconsideration of mental storage capacity , 2001, Behavioral and Brain Sciences.

[4]  Ariel Rubinstein,et al.  On the Interpretation of Decision Problems with Imperfect Recall , 1996, TARK.

[5]  G. A. Miller.  THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

[6]  Andrea Wilson.  Bounded Memory and Biases in Information Processing , 2014 .

[7]  M. Rabin.  Psychology and Economics , 1997 .

[8]  E. Kalai,et al.  The strenght of a little perfection , 1992 .

[9]  Eilon Solan,et al.  Randomization and simplification in dynamic decision-making , 2003, J. Econ. Theory.

[10]  E. Kalai,et al.  Finite Rationality and Interpersonal Complexity in Repeated Games , 1988 .

[11]  A. Neyman.  Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma , 1985 .

[12]  James Dow,et al.  Search Decisions with Limited Memory , 1991 .

[13]  J. Sobel.  A Theory of Credibility , 1985 .

[14]  T. Cover,et al.  Learning with Finite Memory , 1970 .

[15]  T. Cover,et al.  On Memory Saved by Randomization , 1971 .

[16]  Luís M. B. Cabral,et al.  Optimal Brand Umbrella Size , 2007 .

[17]  Itzhak Gilboa,et al.  A Comment on the Absent-Minded Driver Paradox , 1997 .

[18]  Daniel Monte,et al.  Bounded memory and permanent reputations , 2013 .

[19]  Robert J. Aumann,et al.  Repeated Games with Incomplete Information , 1995 .

[20]  Daniel Monte,et al.  Reputation and Bounded Memory in Repeated Games with Incomplete Information , 2007 .

[21]  E. Lehrer.  Repeated Games with Stationary Bounded Recall Strategies , 1988 .

[22]  Yosuke Fukuda,et al.  Rational Cooperation in the Finitely Repeated Prisoners' Dilemma , 2013 .

[23]  Sergiu Hart,et al.  The Absent-Minded Driver , 1996, TARK.

[24]  Ariel Rubinstein,et al.  Finite Automata Play the Repeated Prisoners Dilemma (Now published in Journal of Economic Theory, No.39 (1986),pp.176-188.) , 1985 .