Universal role of migration in the evolution of cooperation

TL;DR

Migration universally influences cooperation in spatial evolutionary games, enhancing it at low levels by strengthening cooperator clusters, but hindering it at high levels by preventing cluster formation.

Contribution

This study reveals the universal impact of unbiased migration on cooperation across various spatial structures, highlighting its dual role depending on migration intensity.

Findings

Low migration enhances cooperation by strengthening cooperator clusters.

High migration prevents cooperator cluster formation, reducing cooperation.

Migration's role is consistent across different spatial structures.

Abstract

We study the role of unbiased migration in cooperation in the framework of spatial evolutionary game on a variety of spatial structures, involving regular lattice, continuous plane and complex networks. A striking finding is that migration plays a universal role in cooperation, regardless of the spatial structures. For high degree of migration, cooperators cannot survive due to the failure of forming cooperator clusters to resist attacks of defectors. While for low degree of migration, cooperation is considerably enhanced compared to statically spatial game, which is due to the strengthening of the boundary of cooperator clusters by the occasionally accumulation of cooperators along the boundary. The cooperator cluster thus becomes more robust than that in static game and defectors nearby the boundary can be assimilated by cooperators, so the cooperator cluster expands, which facilitates cooperation. The general role of migration will be substantiated by sufficient simulations associated with heuristic explanations.