Collapse of cooperation in evolving games

Game theory provides a quantitative framework for analyzing the behavior of rational agents. The Iterated Prisoner’s Dilemma in particular has become a standard model for studying cooperation and cheating, with cooperation often emerging as a robust outcome in evolving populations. Here we extend evolutionary game theory by allowing players’ payoffs as well as their strategies to evolve in response to selection on heritable mutations. In nature, many organisms engage in mutually beneficial interactions and individuals may seek to change the ratio of risk to reward for cooperation by altering the resources they commit to cooperative interactions. To study this, we construct a general framework for the coevolution of strategies and payoffs in arbitrary iterated games. We show that, when there is a tradeoff between the benefits and costs of cooperation, coevolution often leads to a dramatic loss of cooperation in the Iterated Prisoner’s Dilemma. The collapse of cooperation is so extreme that the average payoff in a population can decline even as the potential reward for mutual cooperation increases. Depending upon the form of tradeoffs, evolution may even move away from the Iterated Prisoner’s Dilemma game altogether. Our work offers a new perspective on the Prisoner’s Dilemma and its predictions for cooperation in natural populations; and it provides a general framework to understand the coevolution of strategies and payoffs in iterated interactions. Significance This study offers a new perspective on an age-old question: When does cooperation emerge in populations? Two-player games used to study this question produce an array of counterintuitive results. And yet a consensus has emerged that, in an evolving population, cooperation tends to triumph over cheating––through reciprocity and generosity. But, what happens when players can influence not only their tendencies to cooperate, but also the rewards they reap for cooperation? We analyze coevolution of strategies and payoffs and find that, as individuals maximize the benefits of cooperation, they often pave the way for its collapse. Our analysis provides a framework for studying the coevolution of games and strategies, and suggests that maintaining cooperation may be more difficult than previously thought.