Emergence and Stability of Self-Evolved Cooperative Strategies using Stochastic Machines

Abstract

To investigate the origin of cooperative behaviors, we developed an evolutionary model of sequential strategies and tested our model with computer simulations. The sequential strategies represented by stochastic machines were evaluated through games of iterated Prisoner's Dilemma (PD) with other agents in the population, allowing bootstrapping evolution to occur. We expanded upon past works by proposing a novel mechanism to mutate stochastic Moore machines that introduces a greater spectrum of evolvable machines. These machines were then subjected to various selection mechanisms and the resulting evolved strategies were analyzed. We found that cooperation can indeed emerge spontaneously in evolving populations playing iterated PD, specifically in the form of trigger strategy. In addition, the strategy was found to be resilient towards mutation and thus is evolutionarily stable. To verify the validity of the proposed mutation mechanism, we also evolved the machines to play other 2x2 games such as Chicken and Stag's Hunt, and obtained interesting strategies that demonstrate a degree of Pareto optimality.