Coevolutionary games on networks

Ebel, Holger; Bornholdt, Stefan

doi:10.1103/physreve.66.056118

Cited by 270 publications

(187 citation statements)

References 34 publications

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“…There is much current interest to study evolutionary game dynamics on graphs, which also leads to non-uniform interaction rates. [Ellison, 1993, Nakamaru et al, 1997& 1998, Epstein, 1998, Abramson & Kuperman, 2001, Ebel & Bornholdt, 2002, Szabo & Vukov, 2004, Ifti & et al, 2004, Nakamaru & Iwasa, 2005, Lieberman et al, 2005 The fundamental Lotka-Volterra equation of ecology is equivalent to the replicator equation of evolutionary game theory [Hofbauer & Sigmund, 2003].…”

Section: Resultsmentioning

confidence: 99%

Evolutionary game dynamics with non-uniform interaction rates

Taylor

Nowak

2006

Theoretical Population Biology

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The classical setting of evolutionary game theory, the replicator equation, assumes uniform interaction rates. The rate at which individuals meet and interact is independent of their strategies. Here we extend this framework by allowing the interaction rates to depend on the strategies. This extension leads to nonlinear fitness functions. We show that a strict Nash equilibrium remains uninvadable for non-uniform interaction rates, but the conditions for evolutionary stability need to be modified. We analyze all games between two strategies. If the two strategies coexist or exclude each other, then the evolutionary dynamics do not change qualitatively, only the location of the equilibrium point changes. If, however, one strategy dominates the other in the classical setting, then the introduction of non-uniform interaction rates can lead to a pair of interior equilibria. For the Prisoner's Dilemma, non-uniform interaction rates allow the coexistence between cooperators and defectors. For the snowdrift game, non-uniform interaction rates change the equilibrium frequency of cooperators.

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Section: Resultsmentioning

confidence: 99%

Evolutionary game dynamics with non-uniform interaction rates

Taylor

Nowak

2006

Theoretical Population Biology

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“…In all these cases, however, individuals cannot influence how often they will interact and how long particular interactions will last. On the other hand, other studies have explored the possibility of individuals meeting assortatively, by means of selective partner choice (Eshel and Cavalli-Sforza, 1982;Noë and Hammerstein, 1994;Skyrms and Pemantle, 2000;Bala and Goyal, 2001;Ebel and Bornholdt, 2002;Eguiluz et al, 2005;Biely et al, 2005) or by means of volunteering participation (Peck and Feld-man, 1986;Hauert et al, 2002;Szabó and Hauert, 2002;Hauert and Szabó, 2003;Aktipis, 2004).…”

Section: Introductionmentioning

confidence: 99%

Active linking in evolutionary games

Pacheco

Traulsen

Nowak

2006

Journal of Theoretical Biology

234

170

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In the traditional approach to evolutionary game theory, the individuals of a population meet each other at random, and they have no control over the frequency or duration of interactions. Here we remove these simplifying assumptions. We introduce a new model, where individuals differ in the rate at which they seek new interactions. Once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. In a limiting case, the linking dynamics introduces a simple transformation of the payoff matrix. We outline conditions for evolutionary stability. As a specific example, we study the interaction between cooperators and defectors. We find a simple relationship that characterizes those linking dynamics which allow natural selection to favor cooperation over defection.

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“…Inspired by the seminal paper introducing games on grids [18], evolutionary games on graphs and complex networks [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] have proven instrumental in raising the awareness of the fact that relaxing the simplification of well-mixed interactions may lead to qualitatively different results that are due to pattern formation and intricate organization of the competing strategies, which reveals itself in most unexpected ways. Specifically for the spatial public goods game [38,39], it has recently been shown that inhomogeneous player activities [40], appropriate partner selection [41,42], diversity [43][44][45], the critical mass [46], heterogeneous wealth distributions [47], the introduction of punishment [48,49] and reward [50], as well as both the joker [51] and the Matthew effect [52], can all substantially promote the evolution of public cooperation.…”

Section: Introductionmentioning

confidence: 99%

Conditional strategies and the evolution of cooperation in spatial public goods games

Szolnoki¹,

Perc²

2012

Phys. Rev. E

152

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The fact that individuals will most likely behave differently in different situations begets the introduction of conditional strategies. Inspired by this, we study the evolution of cooperation in the spatial public goods game, where besides unconditional cooperators and defectors, also different types of conditional cooperators compete for space. Conditional cooperators will contribute to the public good only if other players within the group are likely to cooperate as well, but will withhold their contribution otherwise. Depending on the number of other cooperators that are required to elicit cooperation of a conditional cooperator, the latter can be classified in as many types as there are players within each group. We find that the most cautious cooperators, such that require all other players within a group to be conditional cooperators, are the undisputed victors of the evolutionary process, even at very low synergy factors. We show that the remarkable promotion of cooperation is due primarily to the spontaneous emergence of quarantining of defectors, which become surrounded by conditional cooperators and are forced into isolated convex "bubbles" from where they are unable to exploit the public good. This phenomenon can be observed only in structured populations, thus adding to the relevance of pattern formation for the successful evolution of cooperation.

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Coevolutionary games on networks

Cited by 270 publications

References 34 publications

Evolutionary game dynamics with non-uniform interaction rates

Evolutionary game dynamics with non-uniform interaction rates

Active linking in evolutionary games

Conditional strategies and the evolution of cooperation in spatial public goods games

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