How Wealth Accumulation Can Promote Cooperation

Abstract

Explaining the emergence and stability of cooperation has been a central challenge in biology, economics and sociology. Unfortunately, the mechanisms known to promote it either require elaborate strategies or hold only under restrictive conditions. Here, we report the emergence, survival, and frequent domination of cooperation in a world characterized by selfishness and a strong temptation to defect, when individuals can accumulate wealth. In particular, we study games with local adaptation such as the prisoner's dilemma, to which we add heterogeneity in payoffs. In our model, agents accumulate wealth and invest some of it in their interactions. The larger the investment, the more can potentially be gained or lost, so that present gains affect future payoffs. We find that cooperation survives for a far wider range of parameters than without wealth accumulation and, even more strikingly, that it often dominates defection. This is in stark contrast to the traditional evolutionary prisoner's dilemma in particular, in which cooperation rarely survives and almost never thrives. With the inequality we introduce, on the contrary, cooperators do better than defectors, even without any strategic behavior or exogenously imposed strategies. These results have important consequences for our understanding of the type of social and economic arrangements that are optimal and efficient.

Short Versus Long Term Benefits and the Evolution of Cooperation in the Prisoner's Dilemma Game

“…Recently, Chadefaux and Helbing [26] proposed a mechanism of wealth accumulation to support cooperation. In their model wealth is created endogenously from game interactions.…”

“…In many ways [26] is also the starting point of this paper. I propose a model in which agents consider differently weighted accumulated (and suitably normalized) payoffs of their opponents as the basis of decisions for strategy adoption.…”

“…I propose a model in which agents consider differently weighted accumulated (and suitably normalized) payoffs of their opponents as the basis of decisions for strategy adoption. Suitable normalization of payoffs and constant payoffs in the game exclude the mechanism of wealth heterogeneity described in [26] as the mechanism responsible for cooperation.…”

The coevolution of costly heterogeneities and cooperation in the prisoner’s dilemma game

“…Examples range from simple microorganisms (Crespi, 2001) up to complex social interactions in society (Beinhocker, 2007). Various aspects of understanding the emergence and sustainability of such behaviour still poses a major challenge to evolutionary game theory (Weibull, 1996) and recent decades have seen very active research in the field Szolnoki et al, 2009a;Szolnoki and Szabo, 2004;Tanimoto and Yamauchi, 2010;Masuda, 2007;Abramson and Kuperman, 2001;Tanimoto and Yamauchi, 2012;Santos et al, 2006a;Zimmermann and Eguíluz, 2005;Brede, 2011b;Perc and Wang, 2010;Wang and Perc, 2010;Szolnoki et al, 2009b;Szolnoki and Szabó, 2007;Brede, 2011a;Cao et al, 2011;Zhang et al, 2010;Szolnoki et al, 2010;Szolnoki and Perc, 2008;Szabo and Hauert, 2002;Perc and Szolnoki, 2008;Santos et al, 2006b;Brede, 2013b;Van Segbroeck et al, 2009;Szolnoki et al, 2012;Chadefaux and Helbing, 2010).…”

Decelerated invasion and waning-moon patterns in public goods games with delayed distribution

“…Previous research showed that the diversity in reproduction time scales [20] and the coevolution of time scales [21] both promote cooperation. Indirect ways of altering the time scales, for example, by means of breaking the symmetry between interaction and replacement [22], wealth accumulation [23], consideration of long-term benefits [24], or other coevolutionary processes [25][26][27], have also been noted as beneficial for resolving social dilemmas. The application of a delayed distribution of accumulating goods, however, cannot be considered as a simple separation of time scales between learning (strategy adoption) and interaction (payoff accumulation) processes because cooperators, as we will see, lose their payoff permanently between two consecutive distributions, while the effective payoff of defectors remains unchanged.…”