Punish, but not too hard: how costly punishment spreads in the spatial public goods game

By Dirk Helbing, Attila Szolnoki, Matjaz Perc, György Szabó. 2010

400 citations recorded by the source corpus.

We study the evolution of cooperation in spatial public goods games where, besides the classical strategies of cooperation (C) and defection (D), we consider punishing cooperators (PC) or punishing defectors (PD) as an additional strategy. Using a minimalist modeling approach, our goal is to separately clarify and identify the consequences of the two punishing strategies. Since punishment is costly, punishing strategies lose the evolutionary competition in case of well-mixed interactions. When spatial interactions are taken into account, however, the outcome can be strikingly different, and cooperation may spread. The underlying mechanism depends on the character of the punishment strategy. In the case of cooperating punishers, increasing the fine results in a rising cooperation level. In contrast, in the presence of the PD strategy, the phase diagram exhibits a reentrant transition as the fine is increased. Accordingly, the level of cooperation shows a non-monotonous dependence on the fine. Remarkably, punishing strategies can spread in both cases, but based on largely different mechanisms, which depend on the cooperativeness (or not) of punishers.

Subfields: Management Science and Operations Research, Sociology and Political Science, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c3250c3e7352da9c27454a64678741f67fea15a5

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Citations in the corpus

Cooperation Emergence under Resource-Constrained Peer Punishment (2016, background): “To study these effects, Helbing et al. [17] show that the addition of punishing strategies to a classical public goods game, to allow rewarding cooperators or punishing defectors, increases cooperation among the entire population in the case of well-mixed interactions.”
Statistical physics of human cooperation (2017, background): “In addition to continuous phase transitions, discontinuous phase transitions are also common in models of human cooperation, occurring for example as a consequence of indirect territorial competition [110], or the spontaneous emergence of cyclic dominance [60,192].”
Evolutionary dynamics of group interactions on structured populations: a review (2013, background): “The complexity of solutions in spatial public goods games with three or more competing strategies is indeed fascinating, which can be corroborated further by results reported recently for peer-punishment [59–61], pool-punishment [62,63], the competition between both [64] and for reward [65].”
Second-order freeriding on antisocial punishment restores the effectiveness of prosocial punishment (2017, result): “An exciting question now is what if the network reciprocity alone is not strong enough to support the coexistence of cooperators and defectors? Although previous research has shown that prosocial punishment can be effective if the imposed fines are sufficiently high [66, 67], this results was obtain”