Zero-determinant strategies in finitely repeated games

JOURNAL OF THEORETICAL BIOLOGY

卷:438

Article

Ichinose, Genki¹  Masuda, Naoki² 

[1] Shizuoka Univ, Dept Math & Syst Engn, Naka Ku, 3-5-1 Johoku, Hamamatsu, Shizuoka 4328561, Japan

[2] Univ Bristol, Dept Engn Math, Merchant Venturers Bldg,Woodland Rd, Bristol BS8 1UB, Avon, England

关键词: Prisoner's dilemma game;    Cooperation;    Direct reciprocity;    Discount factor;   

DOI  :  10.1016/j.jtbi.2017.11.002

来源: Elsevier

【 摘 要 】

Direct reciprocity is a mechanism for sustaining mutual cooperation in repeated social dilemma games, where a player would keep cooperation to avoid being retaliated by a co-player in the future. So-called zero-determinant (ZD) strategies enable a player to unilaterally set a linear relationship between the player's own payoff and the co-player's payoff regardless of the strategy of the co-player. In the present study, we analytically study zero-determinant strategies in finitely repeated (two-person) prisoner's dilemma games with a general payoff matrix. Our results are as follows. First, we present the forms of solutions that extend the known results for infinitely repeated games (with a discount factor w of unity) to the case of finitely repeated games (0 < w < 1). Second, for the three most prominent ZD strategies, the equlizers, extortioners, and generous strategies, we derive the threshold value of w above which the ZD strategies exist. Third, we show that the only strategies that enforce a linear relationship between the two players' payoffs are either the ZD strategies or unconditional strategies, where the latter independently cooperates with a fixed probability in each round of the game, proving a conjecture previously made for infinitely repeated games. (C) 2017 The Authors. Published by Elsevier Ltd.

【 授权许可】

Free