Zero-determinant strategies in repeated prisoner's dilemma games

Genki Ichinose*, Naoki Masuda

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review


Direct reciprocity is one of the mechanisms for sustaining mutual cooperation in repeated social dilemma games. Zero-determinant (ZD) strategies allow 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. The original ZD strategies were derived for infinitely repeated games. Here, we analytically search for ZD strategies in finitely repeated prisoner's dilemma games. Our results can be summarized as follows. First, we present the forms of ZD in finitely repeated games, which are directly extended from the known results for infinitely repeated games. Second, for the three most notable ZD strategies, the equalizers, extortioners, and generous strategies, we derive the threshold discount factor value above which the ZD strategies exist. Finally, we show that the only strategy sets that enforce a linear payoff relationship are either the ZD strategies or unconditional strategies.

Original languageEnglish
Number of pages2
Publication statusPublished - 2020
Externally publishedYes
Event2018 Conference on Artificial Life: Beyond AI, ALIFE 2018 - Tokyo, Japan
Duration: 2018 Jul 232018 Jul 27


Conference2018 Conference on Artificial Life: Beyond AI, ALIFE 2018

ASJC Scopus subject areas

  • Modelling and Simulation


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