Understanding the effects of asymmetry and relatedness on social volunteerism

I am proud to announce the recent publication of a new paper in the Chinese Science Bulletin with collaborators from Yunnan University and the Kunming Institute of Zoology in Kunming, China. Our paper, entitled “Cooperation in an asymmetric volunteer’s dilemma game with relatedness“, uses a game-theoretic analysis of a new variant to the volunteer’s dilemma to shed light on how commonly-observed social phenomena influence the likelihood of social cooperation.

The volunteer’s dilemma (VoD) is a well-known game theory construct first introduced by Diekmann (1985). In its most simple variant, in order to achieve (or preserve) some common social good at least one individual must volunteer to pay a cost. Like other games of this sort, it is assumed that players make simultaneous choices and that unanimous defection (defined as no one volunteering) creates a “tragedy of the commons”. Previous work on the VoD had explored the role that asymmetrical interaction and relatedness play in determining the likelihood of volunteering by different players. Diekmann (1993) showed that counter-intuitively, players with higher cost-to-benefit ratios (s0-called “weak” players) are less likely to defect. His work also showed that individual defection probabilities increase with group size, although because only one volunteer is required to produce the common good increased defection probabilities do not necessarily lead to decreased common good production in larger groups. Recently, Archetti (2009a) showed that there is an optimal group size that maximizes the probability of producing the common good without wasting effort by having multiple players volunteer (optimally, one player volunteers per round of play, which maximizes overall payoff but assures that payoff is never lost). Archetti also explored the role that relatedness can play in the VoD (Archetti 2009b), demonstrating that while relatedness can decrease the probability of defection, it generally does not get rid of the problem that in larger groups a tragedy of the commons is more likely to occur.

Our work builds on the foundational work of Diekmann and Archetti by asking whether combining asymmetrical interaction and relatedness changes the predicted outcome of the VoD. In particular we would like to know if this effect is synergistic: if the interaction of asymmetry and relatedness goes beyond being a simple additive effect. This question has direct bearing on a variety of intraspecific mutualisms in which related members of the social group experience different cost-to-benefit ratios. For example, meerkats (Suricata suricatta) and eusocial insects are generally closely related and hierarchical in social structure, suggesting that our model might be a reasonable approximation of these animal societies. Our paper shows that relatedness and asymmetry do not produce a synergistic effect on volunteerism: while relatedness does increase the likelihood of volunteerism, its effects on the asymmetric VoD are comparable to its previously-demonstrated effects on the symmetric VoD (Archetti 2009b). While these are perhaps not remarkable results, they do serve to further our understanding of the role of these two important social factors in social dilemmas.

This article is my first foray into the worlds of game theory and evolutionary modeling, and I certainly do not intend to make this my last. Increasingly I am interested in models that explore how ecological interactions produce evolutionary outcomes. Games and other means of exploring interaction (such as individual-based modeling) have the potential to explain the mechanisms that underly natural selection, and will allow us to go beyond simply measuring the strength of selection to explaining why a selective advantage for a particular behavioral trait exists.

This paper came very close to being published in a higher impact journal, but in the end fell short. Although the Chinese Science Bulletin is not a well-known journal, it is open access, and I am proud that this article is available for all with an internet connection to read.