The role of diversity in the evolution of cooperation

Abstract

Understanding the evolutionary mechanisms that promote and maintain cooperative behavior is recognized as a major theoretical problem where the intricacy increases with the complexity of the participating individuals. This is epitomized by the diverse nature of Human interactions, contexts, preferences and social structures. Here we discuss how social diversity, in several of its flavors, catalyzes cooperative behavior. From the diversity in the number of interactions an individual is involved to differences in the choice of role models and contributions, diversity is shown to significantly increase the chances of cooperation. Individual diversity leads to an overall population dynamics in which the underlying dilemma of cooperation is changed, benefiting the society as whole. In addition, we show how diversity in social contexts can arise from the individual capacity for organizing their social ties. As such, Human diversity, on a grand scale, may be instrumental in shaping us as the most sophisticated cooperative entities on this planet.

Introduction

Merriam Webster defines diversity as “the condition of having or being composed of differing elements”. Considering the broad scope of the term, it may legitimately be pointed out that the title of this manuscript is perhaps far more presumptuous than its actual contents. Indeed, we scratch at most of the surface of diversity in its relation to the evolution of cooperation. Even so, we find something that may be seen at first as counter-intuitive: Diversity promotes the evolution of cooperation. Or, at least, when one considers the different aspects of diversity that have been investigated so far.

Historically, the evolution of cooperation has been studied in the absence of diversity (Hardin, 1968, Axelrod and Hamilton, 1981, Hofbauer and Sigmund, 1998, Nowak and Sigmund, 2004, Nowak, 2006b, Nowak, 2006a, Sigmund, 2010). It was found more reasonable to deal with the evolution of cooperation in a population of (primitively) identical individuals, as defined by conventional evolutionary game theory (EGT) (Maynard-Smith, 1982, Hofbauer and Sigmund, 1998, Sigmund, 2010). Every individual can potentially interact with anybody else in an infinite population, having access to the same portfolio of actions (a.k.a. strategies): for instance, to cooperate or to defect. Such cooperators (Cs) and defectors (Ds) typically engage in binary encounters where success is determined by games like the (in)famous Prisoner's dilemma (PD), in which case the evolutionary dynamics relentlessly condemns Cs to extinction. Even when spatial reciprocity (Axelrod, 1984, Nowak and May, 1992, Szabó and Fáth, 2007) was unveiled as a viable mechanism for the emergence of cooperation, Cs and Ds were lined up in an ordered, military-like parade with toroidal endings (for the muse of mathematicians) where each myopic agent interacted only with her four (or eight) immediate neighbors (see for instance Fig. 1B). As such every agent was topologically identical to any other agent in the population. The success of this framework was immense since it showed that cooperation is evolutionary viable within a narrow window of game parameters. Still this approach ignored something as natural as diversity in the neighborhood structure (Amaral et al., 2000, Albert and Barabási, 2002, Dorogotsev and Mendes, 2003, Onnela et al., 2007). Indeed, empirical studies have shown that modern societies are grounded in strongly diverse and heterogeneous networks of exchange and cooperation, in which some individuals play radically different roles depending on their social position, which may or may not be related to the number of actual interactions (see example in Fig. 1a). Incorporating this diversity into the EGT context introduced differences in the way the dilemma is perceived by each individual (Santos and Pacheco, 2005, Santos and Pacheco, 2006, Santos et al., 2011, Pacheco et al., 2009a), as it becomes contingent on her social context. Within EGT, this diversity in interaction patterns is only a first form. In addition, diversity can also exist in the collection of strategic and learning behaviors. In case of the first, we will address in the following the effect of differences in cooperative investment (Santos et al., 2011, Pacheco et al., 2009a). In case of the latter, some individuals, may simply be chosen more frequently as role models than others, producing a significant effect in the flow of behavioral changes caused by the evolutionary dynamics. In addition, diversity in individuals' game strategy (McNamara et al., 2004), imitation capacity (Szolnoki and Szabó, 2007, Perc and Szolnoki, 2008, Szolnoki and Perc, 2008, Szolnoki et al., 2008c) or learning approach (Van Segbroeck et al., 2010b) may produce significantly different outcomes in equivalent games.

As we show in the following, the combined effects resulting from heterogeneous social interactions may lead not only to a boost in the overall levels of cooperation (Abramson and Kuperman, 2001, Santos and Pacheco, 2005, Santos and Pacheco, 2006, Santos et al., 2006b, Santos et al., 2008, Gómez-Gardeñes et al., 2007, Masuda, 2007, Poncela et al., 2007, Szabó and Fáth, 2007, Szolnoki et al., 2008b, Perc and Szolnoki, 2010), but also to a symmetry breaking of the game itself, as well as the introduction of large variance in the distribution of wealth, associated here with the ensuing accumulated game payoffs (Santos et al., 2008, Pacheco et al., 2009a).

After showing how the combined influence of both the number and frequency of interactions contributes to enlarge the chances of Cs, one may naturally wonder what are the origins of such diversity. To address this point, let us imagine for a second that individuals engage in a game of cooperation. Both Cs and Ds prefer to interact with Cs, given the benefit of such an interaction for their own payoff. Let us imagine each individual has the choice to break up the links with those who “hurt” her, maintaining the links with those that do not. Figs. 1b and c show what happens.

As soon as individuals have a choice, the corseted symmetry of the underlying network of contacts is broken, no matter how they break the contacts or to whom they re-direct their attention. In other words, diversity in frequency and number of interactions emerges naturally when humans make decisions, even when one starts from a non-diverse setup (Skyrms and Pemantle, 2000, Ebel and Bornholdt, 2002, Eguiluz et al., 2005, Pacheco et al., 2006a, Santos et al., 2006a, Hanaki et al., 2007, Tanimoto, 2007, Gross and Blasius, 2008, Szolnoki et al., 2008a, Poncela et al., 2009, Szolnoki and Perc, 2009, Van Segbroeck et al., 2009). Clearly, the so-called heterogeneous networks, which arise naturally whenever people make decisions, constitute an ubiquitous feature of the pattern of contacts between individuals in general, and humans in particular, whenever individuals may impose their preferences in what concerns their social ties. In the following sections, we will show that diversity, in its different guises, promotes cooperation.