The shared reward dilemma on structured populations

Abstract

In this paper we study the recently introduced "shared reward dilemma" (Cuesta et al. in J Theor Biol 251:253 263, 2008) in the presence of a structure governing the interactions among the population. The shared reward dilemma arises when the prisoner's dilemma is supplemented with a second stage in which a fixed reward is equally distributed among all cooperators. We first extend our previous results on the equilibrium structure of this game to the case of a one-shot game taking place on a regular network. Subsequently, we consider an evolutionary version of the game on both lattices and random networks. We show that the evolutionary game on graphs exhibits important differences with the case of well-mixed populations. In particular, there exists an important parameter range in which the cooperation is boosted and a single cooperator can invade a population of defectors. We study the dependence of the cooperation levels on the neighborhood size, finding that on random networks the level of cooperation reached decreases as the neighborhood size increases. Moreover, square lattices favor cooperation more than random networks, and on them cooperation may be almost full for certain parameter regions even for large neighborhood sizes. Further, we show that the effect of the population structure is never detrimental for cooperation. We interpret our results in terms of weak versus strong temptation and discuss the nontrivial issues involved in trying to promote cooperation exogenously by means of such a reward mechanism.

Navigating Organization Dynamics: The Real-World Example of Condominium Life in Sicily During the COVID-19 Era in Late 2022-2023

“…equity, and the effective distribution of resources. In line with reference [11], it will also be demonstrated that residents within the condominium community may prioritize their self-interests and opportunistic behaviors over collective well-being. They can act in their own self-interest, potentially leading to outcomes where collective well-being is compromised in favor of personal gain.…”

Shared rewarding overcomes defection traps in generalized volunteer's dilemmas

“…It is worthwhile to point out that, in the generalized 𝑁-person volunteer's dilemma, the public good is produced or safeguarded as a step function of individual contributions. This function thus differs from the linear function used in some previous works (Cuesta et al, 2008;Jiménez et al, 2008;Jiménez et al, 2009) on the 𝑁-person prisoner's dilemma game. In comparison to the case considered here, the N-person prisoner's dilemma can be considered as an extreme case, which − due to the assumed linearity − cannot capture the effects of thresholds for the production of the public good.…”

The public goods game with a new form of shared reward

“…In this setting, players interact through a game, while cooperators can also receive an additional payo coming from an exogenous source available only to them and not to defectors. This updated model therefore incurs a new dilemma: individuals may prefer to choose the shared reward despite the possibility of being exploited by defectors; on the other hand, if too many players do that, cooperators will gain a poor reward and defectors will thus outperform them [39]. Besides, a growing number of field and experimental studies focus on solving collective action problems [40][41][42].…”