Changes in Prisoner´s Dilemma Strategies Over Evolutionary Time With Different Population Sizes

Prisoner´s dilemma is a simple game used for studying cooperation and conflict. This study evolves Prisoner´s dilemma strategies represented by 20-state finite state machines. The resulting strategies are difficult to analyze. It is not obvious looking at a finite state diagram how a machine will behave, and many different machines can represent the same strategy. This study uses a technique called fingerprinting to characterize the strategies. Thirty runs were done for each of three different population sizes for up to 65,536 generations and saved at different stages of evolution. A large diversity of strategies were found. Using different population sizes resulted in finding different strategies and finding common strategies in different proportions. Four strategies were found much more frequently than any others: tit-for-tat, always-defect, and two strategies defined in the study and named Fortress3 and Fortress4. A neighbor-joining technique was used to characterize the fifty most frequently found strategies, and they were found to fall into five distinct groups. The distribution of strategies was found to change over evolutionary time with tit-for-tat and always-defect found more often than other strategies in early evolution, and Fortress3 and Fortress4 becoming important later.