Competition and time-dependent behavior in spatial iterated prisoner’s dilemma incorporating adaptive zero-determinant strategies

Abstract

We propose and study the competitiveness of a class of adaptive zero-determinant strategies (ZDSs) in a population with spatial structure against four classic strategies in iterated prisoner’s dilemma. Besides strategy updating via a probabilistic mechanism by imitating the strategy of a better performing opponent, players using the ZDSs can also adapt their strategies to take advantage of their local competing environment with another probability. The adapted ZDSs could be extortionate-like to avoid being continually cheated by defectors or to take advantage of unconditional cooperators. The adapted ZDSs could also be a compliance strategy so as to cooperate with the conditionally cooperative players. This flexibility makes adaptive ZDSs more competitive than nonadaptive ZDSs. Results show that adaptive ZDSs can either dominate over other strategies or at least coexist with them when the ZDSs are allowed to adapt more readily than to imitate other strategies. The effectiveness of the adaptive ZDSs relies on how fast they can adapt to the competing environment before they are replaced by other strategies. The adaptive ZDSs generally work well as they could adapt gradually and make use of other strategies for suppressing their enemies. When adaptation happens more readily than imitation for the ZDSs, they outperform other strategies over a wide range of cost-to-benefit ratios.