Prisoner's Dilemma with Semi-synchronous Updates: Evidence for a First Order Phase Transition

TL;DR

This paper investigates how semi-synchronous updates in the prisoner's dilemma influence cooperation emergence, revealing a first order phase transition from defection to cooperation, with implications for understanding natural systems.

Contribution

It introduces a semi-synchronous update model for prisoner's dilemma and demonstrates a first order phase transition, advancing the understanding of cooperation dynamics.

Findings

Identified a first order phase transition in cooperation levels

Observed a transition from all-defector to mixed states as a function of update probability

Demonstrated the transition as a frozen-chaotic transition using damage spreading

Abstract

Emergence of cooperation in self-centered individuals has been a major puzzle in the study of evolutionary ethics. Reciprocal altruism is one of explanations put forward and prisoner's dilemma has been a paradigm in this context. Emergence of cooperation was demonstrated for prisoner's dilemma on a lattice with synchronous update [Nature, 359, 826 (1992)]. However, the cooperation disappeared for asynchronous update and the general validity of the conclusions was questioned [PNAS, 90, 7716 (1993)]. Neither synchronous nor asynchronous updates are realistic for natural systems. In this paper, we make a detailed study of more realistic system of semi-synchronous updates where pN agents are updated at every time instant. We observe a transition from all-defector state to a mixed state as a function of p. Despite being transition from absorbing state, our studies indicate that it is a first order transition. Furthermore, we used damage spreading technique to demonstrate that, the transition in this system could be classified as a frozen-chaotic transition.