Percolation and cooperation with mobile agents: Geometric and strategy clusters

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.

References in corpus (10)

• Evolutionary games on graphs
• Prediction and predictability of global epidemics: the role of the airline transportation network
• Does mobility decrease cooperation?
• Continuum Percolation Thresholds in Two Dimensions
• If players are sparse social dilemmas are too: Importance of percolation for evolution of cooperation
• Random mobility and spatial structure often enhance cooperation
• Percolation threshold determines the optimal population density for public cooperation
• Evolution of Cooperation among Mobile Agents
• Different reactions to adverse neighborhoods in games of cooperation
• Mobility, fitness collection, and the breakdown of cooperation