TY - JOUR
T1 - Growth of strategy sets, entropy, and nonstationary bounded recall
AU - Neyman, Abraham
AU - Okada, Daijiro
PY - 2009/5
Y1 - 2009/5
N2 - The paper initiates the study of long term interactions where players' bounded rationality varies over time. Time dependent bounded rationality, for player i, is reflected in part in the number ψi (t) of distinct strategies available to him in the first t-stages. We examine how the growth rate of ψi (t) affects equilibrium outcomes of repeated games. An upper bound on the individually rational payoff is derived for a class of two-player repeated games, and the derived bound is shown to be tight. As a special case we study the repeated games with nonstationary bounded recall and show that, a player can guarantee the minimax payoff of the stage game, even against a player with full recall, by remembering a vanishing fraction of the past. A version of the folk theorem is provided for this class of games.
AB - The paper initiates the study of long term interactions where players' bounded rationality varies over time. Time dependent bounded rationality, for player i, is reflected in part in the number ψi (t) of distinct strategies available to him in the first t-stages. We examine how the growth rate of ψi (t) affects equilibrium outcomes of repeated games. An upper bound on the individually rational payoff is derived for a class of two-player repeated games, and the derived bound is shown to be tight. As a special case we study the repeated games with nonstationary bounded recall and show that, a player can guarantee the minimax payoff of the stage game, even against a player with full recall, by remembering a vanishing fraction of the past. A version of the folk theorem is provided for this class of games.
KW - Bounded rationality
KW - Entropy
KW - Nonstationary bounded recall
KW - Repeated games
KW - Strategic complexity
KW - Strategy set growth
UR - http://www.scopus.com/inward/record.url?scp=64749085239&partnerID=8YFLogxK
U2 - 10.1016/j.geb.2008.04.005
DO - 10.1016/j.geb.2008.04.005
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AN - SCOPUS:64749085239
SN - 0899-8256
VL - 66
SP - 404
EP - 425
JO - Games and Economic Behavior
JF - Games and Economic Behavior
IS - 1
ER -