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

Abstract

The emergence of cooperation in self-centered individuals has been a major puzzle in thestudy of evolutionary ethics. Reciprocal altruism is one of the explanations put forwardand the prisoner’s dilemma has been a paradigm in this context. The emergenceof cooperation was demonstrated for the prisoner’s dilemma on a lattice withsynchronous update. However, the cooperation disappeared for asynchronous update andthe general validity of the conclusions was questioned. Neither synchronous norasynchronous updates are realistic for natural systems. In this paper, we make adetailed study of a more realistic system of semi-synchronous updates wherepN agents are updated at every time instant. We observe a transitionfrom an all-defector state to a mixed state as a function ofp. Our studies indicate that despite it being a transition from an absorbing state, it is afirst-order transition. Furthermore, we used a damage spreading technique to demonstratethat the transition in this system could be classified as a frozen–chaotic transition.