Spatial social dilemmas: dilution, mobility and grouping effects with imitation dynamics

TL;DR

This paper systematically studies how spatial structure, agent mobility, and imitation dynamics influence cooperation in social dilemmas like the Prisoner's Dilemma and Snowdrift games, revealing phase transitions and conditions favoring cooperation.

Contribution

It provides an analytical and numerical analysis of phase transitions in spatial social dilemmas considering mobility and grouping effects, highlighting the microscopic processes that promote cooperation.

Findings

Intermediate mobility and occupancy levels can enhance cooperation.

New phases emerge due to the interplay of mobility and spatial structure.

Analytical transition lines match simulations and mean field predictions.

Abstract

We present an extensive, systematic study of the Prisoner's Dilemma and Snowdrift games on a square lattice under a synchronous, noiseless imitation dynamics. We show that for both the occupancy of the network and the (random) mobility of the agents there are intermediate values that may increase the amount of cooperators in the system and new phases appear. We analytically determine the transition lines between these phases and compare with the mean field prediction and the observed behavior on a square lattice. We point out which are the more relevant microscopic processes that entitle cooperators to invade a population of defectors in the presence of mobility and discuss the universality of these results.