Inactive sites and the evolution of cooperation

¹ Departamento de Física, Universidade Federal de Minas Gerais - Caixa Postal 702, CEP 30161-970, Belo Horizonte - MG, Brazil
² Departamento de Física, Universidade Federal de Ouro Preto - Campus Universitário Morro do Cruzeiro, CEP 35400-000, Ouro Preto - MG, Brazil

Received: 11 April 2016
Accepted: 18 October 2016

Abstract

Cooperation is often conditioned on environmental factors. Behaviors may be inactive due to external factors, and yet the trait itself may not change. We study the evolution of cooperation with active and inactive sites. In inactive sites cooperators behave as defectors, receiving but not providing benefits. This unintentional mimicry provides local advantage to cooperation, but also prevents the mutual reinforcement provided by clusters of active cooperators. In general, we found that cooperation is enhanced by inactivity. In particular, if most sites are inactive, cooperation survives even if the temptation to defect is very large. Interestingly, in the square lattice with pairwise comparison rule we found that cooperation is enforced by inactive sites only up to a certain limit.