The effects of aspiration under multiple strategy updating rules on cooperation in prisoner's dilemma game

In the traditional game theory, a widely accepted assumption is that the participants are completely rational and under the condition of complete information. But in the realistic economy experiences, the participants’ conditions of complete rationality and information are usually hard to be fulfilled. The mutations, un-fixed mechanisms, and policy variations usually challenge the process of natural game evolution. In this work, we mainly study how to make the iterative transformation of policy updating rules to maximize their own benefits in the case of heterogeneous updating rules. In particular, a novel mutation mechanism is developed to study the cooperation situation in natural selection by introducing two different proportion groups in the population, one is based on imitation, the other is based on aspiration level, and both proportions can transform each other under certain conditions at the end of each generation. The mutation of the individual mechanism may occur, it is found that the population proportion and individual rule mutation rate have a strong stabilizing effect on population cooperation under this mixed mechanism, and the lower aspiration level has a certain promoting effect on cooperation as well.