Evolution of cooperation among game players with non-uniform migration scopes

In social dilemmas, cooperation among randomly interacting individuals is often hard to achieve. The situation changes if migration takes place, where game structure jointly evolves with the migration from adverse neighborhoods. Here we introduce a framework combining migration with the individual heterogeneity of migration scopes. When faced with a gloomy outlook, some players prefer vacant sites within their adjacent neighborhoods, while others may migrate within the whole network, provided the sites are empty. Thus, we can make a thorough inquiry of the sustainability of cooperation in a spatially distributed population divided by these two groups, and all possible mixtures between them. Our main result is that small-scope migration and suitable population density can gear up high cooperation levels in the midst of dense populations structured by scale-free networks, while large-scope migration and sparsity favor the cooperator clustering among lattice-structured populations. In this sense, the conditions for the emergence of cooperation are prevailingly created by the spatial reciprocity, and migration also has enough potential to help cooperation to prevail in suitable combination of game parameters in dynamics (e.g., population density, the type of interaction structure and also the migration scope).