Abstract: |
Players with one-step memory in an iterated Prisoner's Dilemma game can adaptively change their strategies after playing some games with their opponent. The probability of change of strategies depends on noise levels, the players’ patience (or reaction time), and initial strategies. Players perform partial imitation, since, realistically, they can only imitate what they observe. Patience determines the frequency of a player's possible strategies changes. In this paper, we focus on the evolution of strategies between two major categories of
players whose innate characters belong either to cheaters (traitors) or nice (benevolent) players. We consider them as agents whose characters are fixed, but their detailed genetic makeup can still vary among several types, so that, for example, the cheaters can evolve among different types of cheaters. We observe their evolutions by means of their degree of cooperation, where the variables are initial strategies, noise, and patience. Here, noise is incorporated in a sigmoid function that accounts for errors in learning. The numerical results show interesting features that we can explain heuristically: in the iterated games between an adaptive cheater against a patient nice player in a noisy environment, we observe a minimum degree of cooperation at a specific noise level. |