Probability Punishment in Spatial Optional Public Goods Games

Resumo

In Optional Public Goods Games, at each round time, players can adopt three possible strategies: cooperate, defect, or abstain (loners). Free-riders pose a threat to cooperation even in the absence of loners. To counter this, incentive mechanisms like decentralized (peer punishment) and centralized (pool punishment) sanctions are normally implemented [1, 4]. Following the methodology introduced in [2], where a peer punishment mechanism modifies the strategy payoffs by incorporating a cost of punishment to cooperators and reducing the benefits of defectors, we introduce a probability P₀ determining whether each cooperator becomes a punisher, imposing sanctions on defectors. Specifically, the decision to punish is determined by a Bernoulli random variable X ~ Bernoulli(P₀). More precisely, on one hand, being a punisher cooperator has a cost α for each defector sanctioned, this situation reduces its payoff, on the other hand, if a cooperator is not selected to be a punisher they receive their normal payoff. Punished defectors have their payoff reduced by a fine β imposed by each punishing cooperator, where α < β.