Antisocial rewarding in structured populations

Abstract

Cooperation in collective action dilemmas usually breaks down in the absence of additional incentive mechanisms. This tragedy can be escaped if cooperators have the possibility to invest in reward funds that are shared exclusively among cooperators (prosocial rewarding). Yet, the presence of defectors who do not contribute to the public good but do reward themselves (antisocial rewarding) deters cooperation in the absence of additional countermeasures. A recent simulation study suggests that spatial structure is sufficient to prevent antisocial rewarding from deterring cooperation. Here we reinvestigate this issue assuming mixed strategies and weak selection on a game-theoretic model of social interactions, which we also validate using individual-based simulations. We show that increasing reward funds facilitates the maintenance of prosocial rewarding but prevents its invasion, and that spatial structure can sometimes select against the evolution of prosocial rewarding. Our results suggest that, even in spatially structured populations, additional mechanisms are required to prevent antisocial rewarding from deterring cooperation in public goods dilemmas.

Cost-effective external interference for promoting the evolution of cooperation

“…This individual-based scheme can be considered a more general form of the prevalent models of institutional incentive strategies, such as institutional punishment and reward 35 – 38 , 42 – 46 , which do not take into account the behavioural composition or state of the population. Typically, only the most extreme case is considered where incentives are always provided (punishment for defectors and reward for cooperators), which corresponds to t = N − 1 of the individual-based scheme.…”

Evolution of preferences in structured populations: genes, guns, and culture

“…Weak selection amounts to considering the limit as tends towards 0. 22 Importantly, under weak selection, the matching probabilities, while still depending on the transmission process, do not depend on the strategies x and y (for any population P = hn; X; ; w; i satisfying assumption [M]). The probability for a randomly drawn descendant of an ancestor, be it a resident or mutant, to coexist in its island with k other descendants of the same ancestor is then solely determined by the vital rates in a population in which everybody uses the same strategy x, no matter which.…”

“…Moreover, a transfer of resources to the neighbor alleviates the competition that the neighbor experiences, and the neighbor is related to the donor according to coe¢ cient r (x;x). Hence, the cost of the transfer is reduced by (x) r (x;x), which explains the denominator in (22).…”

“…In other words, con ‡icts between groups reduces spite, and may even reduce it so much that it turns into altruism, i.e., a positive weight is attached to the neighbors'material payo¤s. Indeed, by substituting (27) (for s 0 = 0) and (31) into (22), we obtain:…”

Group size effects in social evolution

“…Within this framework, the stable rest points of the replicator dynamic correspond to evolutionary endpoints, while the unstable rest points signpost the basins of attraction of such evolutionary attractors. Many social dilemmas for which cooperation can be maintained without repeated interactions or genetic assortment have been theoretically studied using this or related formalisms during the last decades (Taylor and Ward, 1982;Palfrey and Rosenthal, 1984;Diekmann, 1985;Boyd and Richerson, 1988;Motro and Eshel, 1988;Dugatkin, 1990;Dixit and Olson, 2000;Goeree and Holt, 2005;Bach et al, 2006;Hauert et al, 2006;Archetti, 2009;Pacheco et al, 2009;Souza et al, 2009;Archetti and Scheuring, 2011;Chen et al, 2013;Van Cleve and Lehmann, 2013;Sasaki and Uchida, 2014;Chen et al, 2015;Peña et al, 2015;Chen et al, 2017;De Jaegher, 2017;dos Santos and Peña, 2017;Kaznatcheev et al, 2017).…”