The evolution of cooperation in structured populations with influence of nature

Cooperation is commonly illustrated as a Prisoner's Dilemma game. Players obtain 1 (reward) for mutual cooperation and $b$ for mutual defection (punishment); in the case in which they choose different strategies, the cooperator obtains 0 (sucker) and the defector obtains $b>1$ (temptation). Although individual self-interest may not favor cooperation, it can evolve if, for example, players interact multiple times adjusting their behavior accordingly to opponent's previous action. In addition to, if individuals interact to each other as in a structured
population (in square lattice, for instance), cooperators can survive by giving origin to clusters; this phenomena is known as spatial reciprocity. However, it happens that sometimes a player, even being a cooperator, is not able to cooperate because of lack of resources (caused by nautral disasters, migration, etc.). In this present work we intend to model the role played by nature setting some nodes of the lattice as empty nodes (inactive nodes). If an individual is in one of this sites, it is not able to do anything once there are no wherewithal there, no matter it is either a cooperator or a defector. We studied the fraction of cooperators on stationary state as a function of both $w$ (fraction of active nodes) and $b$ (tendency of desertion). The authors thank to FAPEMIG, CAPES and CNPq for financial support.