Risk consideration and cooperation in the iterated prisoner’s dilemma

Abstract

This paper investigates the cooperative behavior in the two-player iterated prisoner's dilemma (IPD) game with the consideration of income stream risk. The standard deviation of one-move payoffs for players is defined for measuring the income stream risk, and thus the risk effect on the cooperation in the two-player IPD game is examined. A two-population coevolutionary learning model, embedded with a niching technique, is developed to search optimal strategies for two players to play the IPD game. As experimental results illustrate, risk-averse players perform better than risk-seeking players in cooperating with opponents. In particular, in the case with short game encounters, in which cooperation has been demonstrated to be difficult to achieve in previous work, a high level of cooperation can be obtained in the IPD if both players are risk-averse. The reason is that risk consideration induces players to negotiate for stable gains, which lead to steady mutual cooperation in the IPD. This cooperative pattern is found to be quite robust against low levels of noise. However, with increasingly higher levels of noise, only intermediate levels of cooperation can be achieved in games between two risk-averse players. Games with risk-seeking players get to even lower cooperation levels. By comparing the players' strategies coevolved with and without a high level of noise, the main reason for the reduction in the extent of cooperation can be explained as the lack of contrition and forgiveness of players in the high-noise interactions. Moreover, although increasing encounter length is helpful in improving cooperation in the noiseless and low-noise IPD, we find that it may enforce the absence of contrition and forgiveness, and thus make cooperation even more difficult in the high-noise games.