Similarity based cooperation and spatial segregation

TL;DR

This paper explores a spatial cooperative game based on similarity, revealing segregation, complex patterns like spiral waves, and stabilization mechanisms in a two-dimensional lattice setting.

Contribution

It extends previous mean-field models to a spatial lattice, introduces local tolerance conversion, and analyzes stability and complex behaviors in the game.

Findings

Strong segregation occurs regardless of parameters.

Local tolerance leads to spiral wave patterns.

High cooperation costs destabilize cooperation, but feedback can stabilize it.

Abstract

We analyze a cooperative game, where the cooperative act is not based on the previous behaviour of the co-player, but on the similarity between the players. This system has been studied in a mean-field description recently [A. Traulsen and H. G. Schuster, Phys. Rev. E 68, 046129 (2003)]. Here, the spatial extension to a two-dimensional lattice is studied, where each player interacts with eight players in a Moore neighborhood. The system shows a strong segregation independent on parameters. The introduction of a local conversion mechanism towards tolerance allows for four-state cycles and the emergence of spiral waves in the spatial game. In the case of asymmetric costs of cooperation a rich variety of complex behavior is observed depending on both cooperation costs. Finally, we study the stabilization of a cooperative fixed point of a forecast rule in the symmetric game, which corresponds to cooperation across segregation borders. This fixed point becomes unstable for high cooperation costs, but can be stabilized by a linear feedback mechanism.