Collective Strategies with a Master-slave Mechanism Dominate in Spatial Iterated Prisoner's Dilemma
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The Iterated Prisoner's Dilemma (IPD) can model transactions among individuals in a population, including human cooperation and trust. Research has focused on equilibrium solutions, mutual cooperation and mutual defection, in IPD. The non-equilibrium strategy profile that one player cooperates and the opponent defects is considered to be unstable and temporal. In this research, we show that non-equilibrium strategies can also be dominant in spatial IPD. An example of such non-equilibrium strategy is a so-called Collective Strategy with Master-Slave Mechanism (CSMSM). A CSMSM identifies the opponent by playing a fixed sequence of moves in the first five rounds of IPD. If the opponent has played the same sequence of moves, it is identified as a kin member. Otherwise it is identified as non-kin. A CSMSM always defects against non-kins. There are two roles in the CSMSM group, master and slave. Every CSMSM acts as a master initially. A master may change to a slave with a predefined probability in each generation. When two CSMSMs meet, they will cooperate with each other if both are masters. In the case that one is a master and another is a slave, the slave will cooperate and the master will defect so that the master's payoff is maximized. Simulation results show that CSMSM outperforms well known strategies like Tit-For-Tat and Always Defect in spatial IPD even if there are only a small ratio of CSMSM in the initial population.
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