The prisoner’s dilemma with semi-synchronous updates: evidence for a first-order phase transition

The emergence of cooperation in self-centered individuals has been a major puzzle in the study of evolutionary ethics. Reciprocal altruism is one of the explanations put forward and the prisoner's dilemma has been a paradigm in this context. The emergence of cooperation was demonstrated for the prisoner's dilemma on a lattice with synchronous update. However, the cooperation disappeared for asynchronous update and the general validity of the conclusions was questioned. Neither synchronous nor asynchronous updates are realistic for natural systems. In this paper, we make a detailed study of a more realistic system of semi-synchronous updates where pN agents are updated at every time instant. We observe a transition from an all-defector state to a mixed state as a function of p. Our studies indicate that despite it being a transition from an absorbing state, it is a first-order transition. Furthermore, we used a damage spreading technique to demonstrate that the transition in this system could be classified as a frozen–chaotic transition.

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