Small-world property promotes the evolution of distributive altruism

Introduction The question of how altruism evolves despite selfish behaviors benefitting agents has for many years been the central theme in the fields such as biology, ecology, sociology, economy and psychology. Several mechanisms promoting the evolution of cooperation have been proposed and can be broadly classified into two categories: direct fitness benefits or indirect fitness benefits (West, 2011). The former covers mutually beneficial cooperation, profiting both the actor and the recipient of the behavior (hence not truly altruistic). Altruistic cooperation is explained by the latter: by helping a close relative reproduce, an individual is still passing copies of its genes on to the next generation, albeit indirectly. Two mechanisms allow related individuals to interact: kin discrimination and limited dispersal. The prisoner’s dilemma game has been commonly used in computational studies on the emergence of altruism. Over the past two decades, many researchers investigated its behavior on networks. The two main properties of the network structure were found to favor survival of cooperators. The first one is clustering coefficient. The success of cooperative behavior is maintained by local interactions within a spatial structure, because cooperators can survive and grow only if they form clusters (Nowak and May, 1992). However, an inverse relationship between the formation of clusters and the success of cooperation has also been reported (Hauert and Szabo, 2005). The second network property is degree heterogeneity. Cooperation has been shown to emerge around the largest hub (Pacheco and Santos, 2005). While it seems that the riddle of cooperation has been largely elucidated as above, recent empirical research brings a more refined view of cooperation as not just a single, homogeneous trait but several different traits with different costs, benefits and contexts. Warneken and Tomasello (2009) investigated three types of altruism by comparing behaviors of children and chimpanzees. The three types were: helping (when agents help others achieve their goals), sharing (when agents share valuable goods such as food with others) and informing (when agents share with others things the others need or want to know). They found that although chimpanzees help others instrumentally, they are less likely to share resources at their own expense. Also, they do not share information helpful to others. However, both infants and young children were observed to be helpful, generous, and informative. Thus, the authors suggest that sharing and informing are types of altruism specific to humans. Based on the above, we have proposed the distribution dilemma game (DDG) (Ueno and Arita, 2015) that aims to model the altruism in the distribution of resources (material goods or information), but can also capture the emergent properties of resources. Specifically, DDG can describe both how the total value of a resource is changed when it is distributed among agents and how the value is changed synergistically when an agent owns different kinds of resources. Our preliminary study investigated the behavior of an evolutionary model with DDG on a one-dimensional torus and observed the emergence of altruism in certain scenarios. In this paper, we extend the study by investigating the effects of more realistic interaction networks on the emergence of altruism. Specifically, we focus on the behavior of DDG on small-world network topology.