Study On Zero-determinant Strategies In Iterated Prisoner’s Dilemma Game

Competition and strategy selection between a class of generalized zero determinant strategies and the classic strategies(All C, All D, TFT, WSLS) in the iterated prisoner’s dilemma is studied comprehensively in this thesis. There are extortionate ZD Strategies in the set of ZD strategies, the Player who use the extortionate ZD strategy could get a payoff that is() times that of opponent’s, when the payoff is measured with respect to a reference baseline, i.e., the mutual noncooperation payoff. In this thesis, we generalize the reference baseline by a parameter. By tuning, the reference payoff can be changed from the payoff of mutual cooperation. We present the expected payoffs when ZD strategy competes with each one of the classic strategies and study the strategy evolution which is based on adopting the strategy of a better performing neighbor in a well- mixed population of finite size and a population on a square lattice. Depending o n the parameters, extortion- like strategies may not be evolutionarily stable despite a positive surplus over cooperative strategies, while extortion- like strategies may dominate or coexist with other strategies that tend to defect despite a negative surplus. In a well- mixed population, the dependence of the equilibrium fraction of ZD strategy players on the model parameters in a well- mixed population can be understood analytically by comparing the average payoffs to the competing strategies. The success of the ZD strategy on a square lattice can be qualitatively analyzed by payoff band theory.A class of adaptive zero-determinant strategies is put forward in this thesis. We study the competitiveness of the proposed strategies in a population with spatial str ucture against four classic strategies. Besides strategy updating via a probability mechanism by imitating the strategy of a better performing opponent, players using the ZD Strategies can also adapt their strategies to take advantage of their local compet ing environment with another probability. For avoiding being continually cheated by defectors, the adapted ZD Strategies could be extortionate- like. The adapted ZD Strategies could also be a compliance strategy in order to cooperate with the conditionally cooperative players. This flexibility makes adaptive ZD Strategies more competitive than non-adaptive ZD Strategies. The simulation results show that adaptive ZD Strategies can either dominate over other strategies or at least coexist with them when the ZD Strategies are allowed to adapt more readily than to imitate other strategies.