Punishing untrustworthiness and free riders to maintain cooperation in multi-agent social dilemmas using fuzzy logic

Social dilemmas force individuals to choose between their own self-interests or group interests. Individuals can decide to cooperate for the benefit of the group or defect to put their personal interests first. The Public Goods Games (PGG) is a well-studied economic game that can provide insight into human behavior in social dilemmas. In particular, the question of interest is why do non-kin cooperate in these social dilemmas? Studies have shown that cooperation levels in a population increase if cooperators can punish (e.g., impose a fixed penalty) on free riding defectors to reduce their payoff during a PGG. This punishment is costly because these cooperators must pay a small fee to impose this punishment. Even a minority of cooperators can be successful in punishing so long as cooperators who punish are trustworthy—i.e., the agree to punish and actually do punish—and the punishment levels are high enough. But cooperators may become untrustworthy by refusing to punish to avoid paying the small fee. This second type of free riding can undermine the punishment applied to defectors, allowing them ultimately to prevail in the entire population. Everyone loses in that case. This situation can be avoided by also punishing untrustworthy cooperators. In this paper, replicator equations predict how different strategies evolve in a population of PGG players. We use a 1st-order fuzzy logic system to determine punishment levels applied to untrustworthy cooperators. Our results show a fuzzy logic based decision system can effectively improve cooperation levels in the population.