Evolutionary dynamics of cooperation in a population with probabilistic corrupt enforcers and violators

Abstract

Pro-social punishment is a key driver of harmonious and stable society. However, this institution is vulnerable to corruption since law-violators can avoid sanctioning by paying bribes to corrupt law-enforcers. Consequently, to understand how altruistic behavior survives in a corrupt environment is an open question. To reveal potential explanations here we introduce corrupt enforcers and violators into the public goods game with pool punishment, and assume that punishers, as corrupt enforcers, may select defectors probabilistically to take a bribe from, and meanwhile defectors, as corrupt violators, may select punishers stochastically to be corrupted. By means of mathematical analysis, we aim to study the necessary conditions for the evolution of cooperation in such corrupt environment. We find that cooperation can be maintained in the population in two distinct ways. First, cooperators, defectors, and punishers can coexist by all keeping a steady fraction of the population. Second, these three strategies can form a cyclic dominance that resembles a rock-scissors-paper cycle or a heteroclinic cycle. We theoretically identify conditions when the competing strategies coexist in a stationary way or they dominate each other in a cyclic way. These predictions are confirmed numerically.

Third-Party Punishment or Compensation? It Depends on the Reputational Benefits

“…Other studies have made similar observations (Wang and Chen, 2011 ; Cui et al, 2017 ). Sometimes, the violator even bribe the third-party punishers to avoid being punished (Liu L. et al, 2019 ). Once corruption occurs, the third-party punishers will not only fail to promote cooperation but will undermine it.…”

Conditional cooperation in group contests

“…In an overview, [8] reports that the findings are quite stable across studies, about 61% of participants being classified as conditional cooperators (followed by about 20% of free-riders). This behavior has been described in other related environments, for instance, in collective-risk social dilemmas (a variant of public goods games), where a group must achieve a given threshold through common contributions to avoid a general loss (i.e., as a climate change environment), see [9][10][11]. It is thus natural to assume that this behavior should at least partly explain how individuals behave in group contests, i.e., situations in which members of a group face a social dilemma when competing with other rival groups.…”

Evolution of altruistic punishments among heterogeneous conditional cooperators

“…For example, an agent who reciprocated in PGG can be punished by other reciprocators in the group because the altruistic punishments are implemented by random pairings and based on relative CCC values, not based on the actions of individuals. As noted in the literature, free riders can bribe the altruistic punishers 51 and free riders can be involved in punishing 20,21 . Punishing reciprocators or negative reciprocators might lead to retaliation against the reciprocators or free riding in the next round.…”