Behavioral Diversity, Choices and Noise in the Iterated Prisoner's Dilemma

Abstract

Real-world dilemmas rarely involve just two choices and perfect interactions without mistakes. In the iterated prisoner's dilemma (IPD) game, intermediate choices or mistakes (noise) have been introduced to extend its realism. This paper studies the IPD game with both noise and multiple levels of cooperation (intermediate choices) in a coevolutionary environment, where players can learn and adapt their strategies through an evolutionary algorithm. The impact of noise on the evolution of cooperation is first examined. It is shown that the coevolutionary models presented in this paper are robust against low noise (when mistakes occur with low probability). That is, low levels of noise have little impact on the evolution of cooperation. On the other hand, high noise (when mistakes occur with high probability) creates misunderstandings and discourages cooperation. However, the evolution of cooperation in the IPD with more choices in a coevolutionary learning setting also depends on behavioral diversity. This paper further investigates the issue of behavioral diversity in the coevolution of strategies for the IPD with more choices and noise. The evolution of cooperation is more difficult to achieve if a coevolutionary model with low behavioral diversity is used for IPD games with higher levels of noise. The coevolutionary model with high behavioral diversity in the population is more resistant to noise. It is shown that strategy representations can have a significant impact on the evolutionary outcomes because of different behavioral diversities that they generate. The results further show the importance of behavioral diversity in coevolutionary learning.