The public goods game with a new form of shared reward

Abstract

Altruistic contribution to a common good evenly enjoyed by all group members is hard to explain because of the greater benefits obtained by a defector than a cooperator. A variety of mechanisms have been proposed to resolve the collective dilemma over the years, including rewards for altruism. An underrated and easily ignored phenomenon is that the altruistic behaviors of cooperators not only directly enhance the benefits of their game opponents, but also indirectly produce good influences to other allied members in their surroundings (e.g. relatives or friends). Here we propose a shared reward, in the form of extensive benefits, to extend the traditional definition of the public goods game. Mathematical analysis using the Moran process helps us to obtain the fixation probability for one 'mutant' cooperator to invade and dominate the whole defecting population. Results suggest that a tunable parameter exists, above a certain critical value of which natural selection favors cooperation over defection. In addition, analytical results with replicator dynamics show that this critical value influencing the evolution of altruism is closely correlated with the population size, the gaming group size and the synergy factor of the public goods game. These results, based on an extended notion of shared reward and extensive benefits, are expected to provide novel explanations for the emergence of altruistic behaviors.

Cooperation guided by the coexistence of imitation dynamics and aspiration dynamics in structured populations

“…-Cooperation plays an important role in nature as universally observed in plants, animals and human society [1], and thus it has prompted considerable efforts in the past several decades [2][3][4][5][6][7]. A useful paradigm for investigating this problem is the public goods game (PGG), which captures the group interactions, and focuses on the origin of cooperation in the conflict between individual and collective interest [8][9][10][11][12]. In a typical PGG, the classical game theory predicts that all players defect and the public goods are forgone [13,14].…”

Evolutionary Game Analysis of Participations in Museum Public–Private Partnership Projects Based on System Dynamics

“…Different incentive compensation mechanisms and operating models determine not only their effects on social forces but also the size of the public sector's cooperation costs. Game theory has been used by scholars to study the relevant incentive mechanism [40,41], compensation mechanisms [36], reward models [42,43], income distribution [44], etc., between the public and private sectors in PPP projects. In light of this, this paper examines the current situation of domestic and international PPP projects in the museum field by focusing on museum service practices.…”

Research on Evolutionary Game Analysis of Spatial Cooperation for Social Governance of Basin Water Pollution

“…It is a standardized model that extends the two-person prisoner game to the population interaction, and succinctly describes the multi-person prisoner dilemma, that is, whether the individuals in the population are willing to bear the cooperative costs at the same time to realize the collective interests [26][27][28][29][30]. At present, the public goods game mainly focuses on the individual behavior mechanism [31], the game with spatial structure [32,33], the strategy update mechanism [34,35], and the strengthening mechanism for cooperation promotion [36][37][38][39][40][41][42]. Different from the general public goods game model, the benefits of water pollution treatment usually change with the change of treatment input.…”