Evolution of Cooperation in Prisoner’s Dilemma within Changeable External Environments

Rational individuals make a relatively dominant choice when faced with two opposing options of cooperation and betrayal in interactions. Without other interference, this often leads to a dilemma when social interests and personal interests are inconsistent, like the prisoner’s dilemma. However, in reality, an individual plays multiple games simultaneously. Members of a population may be influenced by other games to modify their strategic choices in the main game. In this paper, we consider intraspecific and interspecific games simultaneously from a multi-game perspective. How intraspecific cooperation evolves when different types of interspecific games as changeable environments is of great interest to us. We scrutinize the evolution of cooperation within the population in the prisoner’s dilemma by replicator dynamics with three different types of external environments of cooperation. The results show that the emergence and maintenance of cooperation in the intraspecific game are related to the relative size and the probability of cooperation in the external environment. Numerical experiences are provided to support the theoretical results.