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Two-Step "Win-Stay, Lose-Shift" And Learning To Cooperate In The Repeated Prisoner'S Dilemma

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  • ARKADY KRYAZHIMSKIY

    (International Institute for Applied Systems Analysis, Laxenburg, Austria;
    Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia)

Abstract

The standardwin-stay,lose-shiftbehavior strategy in the repeated Prisoner's Dilemma game prescribes the players that win and lose in a current game round to keep and to change, respectively, their current actions, in the next round. Winning and losing are understood as receiving one of two upper values and one of two lower values, respectively, among the four admissible values for the players' benefits. In particular, a player acting as a cooperator against cooperation wins and therefore is not allowed to switch to defection in the next round with a hope to gain more (provided his/her rival keeps cooperating). This constraint can be viewed as too strong for a selfish player. Here, we discuss atwo-stepwin-stay, lose-shift behavior that differs from the traditional win-stay lose-shift one in understanding of winning and losing. A player wins if his/her benefit is no smaller that in the previous round, and loses otherwise. This pattern is in a sense more selfish; in particular, a switch from cooperation (against cooperation) to defection is not forbidden. Another confirmation of a more selfish character of the two-step win-stay, lose-shift behavior, compared to the standard win-stay, lose-shift one, is that the former does not bring two individuals playing the repeated Prisoner's Dilemma game to mutual cooperation. In this paper, our goal is to understand to what degree one can relax the two-step win-stay, lose-shift behavior in selfishness so as to reach mutual cooperation, anyway. We deal with two models of the repeated Prisoner's Dilemma game — a game of two individuals and a game in a group of players. In the game of two individuals, a relaxed two-step win-stay, lose-shift behavior assumes that the players use mixed strategies; here, relaxation is associated withpatience. In the game in a group of players, relaxation is achieved throughconformity, a tendency to join the majority. We show that even a small degree of conformity is enough to teach a two-step win-stay, lose-shift group to cooperate.

Suggested Citation

  • Arkady Kryazhimskiy, 2010. "Two-Step "Win-Stay, Lose-Shift" And Learning To Cooperate In The Repeated Prisoner'S Dilemma," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 437-451.
    • Handle: RePEc:wsi:igtrxx:v:12:y:2010:i:04:n:s0219198910002763
    DOI: 10.1142/S0219198910002763
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    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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