Evolutionary dynamics of social dilemmas in structured heterogeneous populations

Abstract

Real populations have been shown to be heterogeneous, in which some individuals have many more contacts than others. This fact contrasts with the traditional homogeneous setting used in studies of evolutionary game dynamics. We incorporate heterogeneity in the population by studying games on graphs, in which the variability in connectivity ranges from single-scale graphs, for which heterogeneity is small and associated degree distributions exhibit a Gaussian tale, to scale-free graphs, for which heterogeneity is large with degree distributions exhibiting a power-law behavior. We study the evolution of cooperation, modeled in terms of the most popular dilemmas of cooperation. We show that, for all dilemmas, increasing heterogeneity favors the emergence of cooperation, such that long-term cooperative behavior easily resists short-term noncooperative behavior. Moreover, we show how cooperation depends on the intricate ties between individuals in scale-free populations.complex networks ͉ evolution of cooperation C ooperation has played a key role throughout evolution (1). Self-replicating cells have cooperated to form multicellular organisms throughout evolutionary history (2, 3). Similarly, we know that animals cooperate in families to raise their offspring and in groups to prey and to reduce the risk of predation (4, 5). Cooperation has been conveniently formulated in the framework of evolutionary game theory, which, when combined with games such as the Prisoner's Dilemma, which is used as a metaphor for studying cooperation between unrelated individuals, enables one to investigate how collective cooperative behavior may survive in a world where individual selfish actions produce better short-term results. Analytical solutions for this problem have been obtained when populations are assumed infinite and their interactions are assumed homogeneous such that all individuals are in equivalent positions. Under such assumptions, noncooperative behavior prevails. Such an unfavorable scenario for cooperation in the Prisoner's Dilemma game, together with the difficulty in ranking the actual payoffs in field and experimental work (6, 7), has lead to the adoption of other games (8, 9), such as the Snowdrift game (also known as Hawk-Dove or Chicken), which is more favorable to cooperation, and the Stag-Hunt game (10), and to numerical studies of cooperation in finite, spatially structured populations (11) in which homogeneity is still retained. Such studies of the role of structured populations have attracted considerable attention, originating from fields ranging from sociology to biology, ecology, economics, mathematics, and physics, to name a few (11)(12)(13)(14)(15)(16)(17)(18)(19). More recently, however, compelling evidence has been accumulated that a plethora of biological, social, and technological real-world networks of contacts (NoC) are mostly heterogeneous (20)(21)(22). Indeed, analysis of real-world NoC (20) has provided evidence for the following (heterogeneous) types: (i) single-scale networks, which are charac...

The mechanics of stochastic slowdown in evolutionary games

“…The study of cooperation in an evolutionary context mainly focuses on mechanism that allow the emergence and maintenance of cooperation (see e.g., Axelrod and Hamilton, 1981;Maynard Smith, 1982b;Nowak, 2006b;Santos et al, 2006;Sigmund et al, 2010;Hilbe and Traulsen, 2012;van Veelen et al, 2012). In well-mixed populations, cooperation cannot be maintained when defection emerges unless mechanisms promoting cooperation are present, such as repetition, punishment, or rewarding.…”

Does mobility decrease cooperation?

“…These spatial games, where the interactions are localized and non random, have been studied and extended in many ways (see, for example, Refs. [1,2,4,9,10,15,19,22,23,24,25,29,30,31,34,37,38,40,41,44,45,46,47,49,52]). Once the population is spatially structured, a natural question concerns the effects of mobility that, along with other important biological factors, is often neglected [28]: is it possible to evolve and sustain cooperation in a population of mobile agents, where retaliation can be avoided by moving away from the former partner?…”

The prisoner’s dilemma on co-evolving networks under perfect rationality

“…In [15] it was shown, that for a variety of dilemmas (including the PD), heterogenous networks (e.g. scale-free networks) favor the emergence of cooperation.…”