Percolation and cooperation with mobile agents: Geometric and strategy clusters

TL;DR

This study investigates how the geometric percolation of contact networks influences the persistence of cooperation and defection among mobile agents playing the Prisoner's Dilemma, revealing that percolation conditions are crucial for survival.

Contribution

It introduces a geometric interpretation of phase transitions in a mobile agent model, highlighting the role of percolation in sustaining cooperation and defection.

Findings

Percolation of the contact network promotes cooperation.

Defector survival depends on the percolation of defector clusters.

Isolated defector groups eventually go extinct without percolation.

Abstract

We study the conditions for persistent cooperation in an off-lattice model of mobile agents playing the Prisoner's Dilemma game with pure, unconditional strategies. Each agent has an exclusion radius rP, which accounts for the population viscosity, and an interaction radius rint, which defines the instantaneous contact network for the game dynamics. We show that, differently from the rP=0 case, the model with finite-sized agents presents a coexistence phase with both cooperators and defectors, besides the two absorbing phases, in which either cooperators or defectors dominate. We provide, in addition, a geometric interpretation of the transitions between phases. In analogy with lattice models, the geometric percolation of the contact network (i.e., irrespective of the strategy) enhances cooperation. More importantly, we show that the percolation of defectors is an essential condition for their survival. Differently from compact clusters of cooperators, isolated groups of defectors will eventually become extinct if not percolating, independently of their size.