Zero-determinant Strategies for Three-player in Finitely Repeated Games

Abstract

Zero-determinant strategies are a new class of probabilistic and conditional strategies, where a player can use a linear relationship between his own payoff and the opponents payoff to determine his opponents expected payoff or extort his opponents unilaterally. This paper will analysis a model of zero-determinant strategies for three players in the finitely repeated public goods game (with a discount factor 6 satisfying 0 < 6 < 1). Via analyzing these strategies for three players in the game, including equalizer strategies, extortion strategies and generous strategies, it finds that a player also has an ability to pin the expected total payoff of all other players in a unilateral way as the two-player model by equalizer strategies and can set a ratio between his payoff and the total payoff of all other players by the extortion strategies, and the expected payoffs of three players can obtain the same payoff when they cooperate in the first round by using generous strategies. This provides potential clues to design efficient cooperation protocol in multi-agent systems.