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33
Participation Costs Dismiss the Advantage of Heterogeneous Networks in Evolution of Cooperation
 Proceedings of the Royal Society B
, 2007
"... Real social interactions occur on networks in which each individual is connected to some, but not all, of others. In social dilemma games, heterogeneity in the number of contacts per player is known to promote evolution of cooperation in a fixed population size. With positively biased payoff structu ..."
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Cited by 22 (2 self)
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Real social interactions occur on networks in which each individual is connected to some, but not all, of others. In social dilemma games, heterogeneity in the number of contacts per player is known to promote evolution of cooperation in a fixed population size. With positively biased payoff structure, which is customarily used in evolutionary games, players with more neighbors play more frequently, earn more, and propagate cooperation to others. However, maintaining a social contact can be costly, and so the gross payoff per participation is not necessarily positive. We show that even a relatively small participation cost extinguishes the advantage of heterogeneous networks. In this situation, more connected players are charged more so that they are no longer spreaders of cooperation. If participation is even more costly, those with fewer contacts win and guide the evolution. Although the baseline payoff modulated by the participation cost is irrelevant in homogeneous networks, it drastically affect evolution on heterogeneous networks. 1
Repeated games and direct reciprocity under active linking
, 2008
"... Direct reciprocity relies on repeated encounters between the same two individuals. Here we examine the evolution of cooperation under direct reciprocity in dynamically structured populations. Individuals occupy the vertices of a graph, undergoing repeated interactions with their partners via the edg ..."
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Cited by 14 (4 self)
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Direct reciprocity relies on repeated encounters between the same two individuals. Here we examine the evolution of cooperation under direct reciprocity in dynamically structured populations. Individuals occupy the vertices of a graph, undergoing repeated interactions with their partners via the edges of the graph. Unlike the traditional approach to evolutionary game theory, where individuals meet at random and have no control over the frequency or duration of interactions, we consider a model in which individuals differ in the rate at which they seek new interactions. Moreover, once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. Whenever the active dynamics of links is sufficiently fast, population structure leads to a simple transformation of the payoff matrix, effectively changing the game under consideration, and hence paving the way for reciprocators to dominate defectors. We derive analytical conditions for evolutionary stability.
Evolutionary stability on graphs
, 2008
"... Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect e ..."
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Cited by 13 (1 self)
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Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs. We obtain analytical conditions for regular graphs of degree k42. Those theoretical predictions are compared with computer simulations for random regular graphs and for lattices. We study three different update rules: birth–death (BD), death–birth (DB), and imitation (IM) updating. Evolutionary stability on sparse graphs does not imply evolutionary stability in a wellmixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs.
A Course in Game Theory
, 1994
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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Cited by 6 (0 self)
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit:
A novel analytical method for evolutionary graph theory problems
, 2013
"... Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are used for estimating such fixation probabilities on general di ..."
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Cited by 3 (0 self)
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Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are used for estimating such fixation probabilities on general directed graphs, since no good analytical methods exist. In this paper, we introduce a novel deterministic framework for computing fixation probabilities for strongly connected, directed, weighted evolutionary graphs under neutral drift. We show how this framework can also be used to calculate the expected number of mutants at a given time step (even if we relax the assumption that the graph is strongly connected), how it can extend to other related models (e.g. voter model), how our framework can provide nontrivial bounds for fixation probability in the case of an advantageous mutant, and how it can be used to find a nontrivial lower bound on the mean time to fixation. We provide various experimental results determining fixation probabilities and expected number of mutants on different graphs. Among these, we show that our method consistently outperforms Monte Carlo simulations in speed by several orders of magnitude. Finally we show how our approach can provide insight into synaptic competition in neurology.
Fast and deterministic computation of fixation probability in evolutionary graphs
 In: CIB ’11: The Sixth IASTED Conference on Computational Intelligence and Bioinformatics (accepted). IASTED
, 2011
"... In evolutionary graph theory [1] biologists study the problem of determining the probability that a small number of mutants overtake a population that is structured on a weighted, possibly directed graph. Currently Monte Carlo simulations are used for estimating such fixation probabilities on direct ..."
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Cited by 3 (1 self)
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In evolutionary graph theory [1] biologists study the problem of determining the probability that a small number of mutants overtake a population that is structured on a weighted, possibly directed graph. Currently Monte Carlo simulations are used for estimating such fixation probabilities on directed graphs, since no good analytical methods exist. In this paper, we introduce a novel deterministic algorithm for computing fixation probabilities for strongly connected directed, weighted evolutionary graphs under the case of neutral drift, which we show to be a lower bound for the case where the mutant is more fit than the rest of the population (previously, this was only observed from simulation). We also show that, in neutral drift, fixation probability is additive under the weighted, directed case. We implement our algorithm and show experimentally that it consistently outperforms Monte Carlo simulations by several orders of magnitude, which can allow researchers to study fixation probability on much larger graphs.
Article Coevolution of Cooperation, Response to Adverse Social Ties and Network Structure
, 2010
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Evolution of Cooperation in a Population of Selfish Adaptive Agents
 Advances in Artificial Life
, 2007
"... Abstract. Often the selfish and strong are believed to be favored by natural selection, even though cooperative interactions thrive at all levels of organization in living systems. Recent empirical data shows that networks representing the social interactions between people exhibit typically high ..."
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Cited by 1 (0 self)
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Abstract. Often the selfish and strong are believed to be favored by natural selection, even though cooperative interactions thrive at all levels of organization in living systems. Recent empirical data shows that networks representing the social interactions between people exhibit typically high average connectivity and associated singletobroadscale heterogeneity, a feature which precludes the emergence of cooperation in any static network. Here, we employ a model in which individuals are able to selforganize both their strategy and their social ties throughout evolution, based exclusively on their selfinterest. The entangled evolution of individual strategy and network structure provides a key mechanism toward the sustainability of cooperation in social networks. The results show that simple topological dynamics reflecting the individual capacity for selforganization of social ties can produce realistic networks of high average connectivity with associated singletobroadscale heterogeneity, in which cooperation thrives. 1