The evolution of altruism by costly punishment in lattice-structured populations: score-dependent viability versus score-dependent fertility

Abstract

Question: What part might punishment play in maintaining cooperation in animal and human societies? Mathematical method: Evolutionary game theory. The game’s score modifies either viability or fertility. Key assumptions: The population is spatially structured. After a player dies, a copy of one of its nearest neighbours fills the vacancy. Altruists may punish selfish individuals by forcing them to pay a ‘fine’, but the punisher itself must pay to impose the fine. Conclusions: Punishment can make altruism an evolutionarily stable strategy. In a well-mixed population, if the score affects fertility, then an altruist-punisher cannot invade a selfish population. But it can invade if the score affects viability and the fine is large. In a spatially structured population, an altruist-punisher can invade a selfish population whether the score affects viability or fertility. In the viability model, large fines promote altruism. But in the fertility model, either a large fine or a high benefit of cooperation promotes altruism.