Evolutionary stability on graphs

Ohtsuki, Hisashi; Nowak, Martin A.

doi:10.1016/j.jtbi.2008.01.005

Cited by 112 publications

(77 citation statements)

References 76 publications

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“…We consider in more detail the special case as given by payoff matrix (20). We suppose further that b < d < a, such that both A and B fulfill Condition (I) for an ESS N .…”

Section: Applications and Discussionmentioning

confidence: 99%

“…If c = b, the first condition in (18) reduces to (19) Hence, we are in the special case of a partnership game with the additional qualification that d is exactly the midpoint of a and b, so that the payoff matrix is given by (20) Note that in order to ensure condition (4), we have to assume that which implies b < a. Now we have to look at the sign of the second-order term …”

Section: Second-order Conditionsmentioning

confidence: 99%

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One-third rules with equality: Second-order evolutionary stability conditions in finite populations

Bomze

Pawlowitsch

2008

Journal of Theoretical Biology

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The one-third law of evolutionary dynamics [Nowak et al. 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 246-650] describes a robustness criterion for evolution in a finite population: If at an A-frequency of 1/3, the fitness of an A player is greater (smaller) than the fitness of a B player, then a single A mutant that appears in a population of otherwise all B has a fixation probability greater (smaller) than the neutral threshold 1/N, the inverse population size. We examine the case where at an A-frequency of 1/3, the fitness of an A player is exactly equal to the fitness of a B player. We find that in this case the relative magnitude of the cross payoffs matters: If the payoff of A against B is larger (smaller) than the payoff of B against A, then a single A mutant has a fixation probability larger (smaller) than 1/N. If the cross payoffs coincide, we are in the special case of a partnership game, where the deviation cost from an inefficient equilibrium is exactly balanced by the potential gain of switching to the payoff dominant equilibrium. We show that in this case the fixation probability of A is lower than 1/N. Finally we illustrate our findings by a language game with differentiated costs of signals.

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“…We consider in more detail the special case as given by payoff matrix (20). We suppose further that b < d < a, such that both A and B fulfill Condition (I) for an ESS N .…”

Section: Applications and Discussionmentioning

confidence: 99%

Section: Second-order Conditionsmentioning

confidence: 99%

One-third rules with equality: Second-order evolutionary stability conditions in finite populations

Bomze

Pawlowitsch

2008

Journal of Theoretical Biology

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“…Additionally, for some models with nontrivial interaction structure, it can be shown that assortment patterns are likely to equilibrate (in some sense) while a mutant is still rare (Matsuda et al, 1992;van Baalen and Rand, 1998;Ferrière and Le Galliard, 2001;Ohtsuki and Nowak, 2008). The invasion fitness can then be derived assuming that such equilibration has occurred.…”

Section: Fixation Probability Versus Invasion Fitnessmentioning

confidence: 99%

Adaptive Dynamics with Interaction Structure

Allen

Nowak

Dieckmann

2013

The American Naturalist

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Evolutionary dynamics depend critically on a population's interaction structure-the pattern of which individuals interact with which others, depending on the state of the population and the environment. Previous research has shown, for example, that cooperative behaviors disfavored in well-mixed populations can be favored when interactions occur only between spatial neighbors or group members. Combining the adaptive dynamics approach with recent advances in evolutionary game theory, we here introduce a general mathematical framework for analyzing the long-term evolution of continuous game strategies for a broad class of evolutionary models, encompassing many varieties of interaction structure. Our main result, the "canonical equation of adaptive dynamics with interaction structure", characterizes expected evolutionary trajectories resulting from any such model, thereby generalizing a central tool of adaptive dynamics theory. Interestingly, the effects of different interaction structures and update rules on evolutionary trajectories are fully captured by just two real numbers associated with each model, which are independent of the considered game. The first, a structure coefficient, quantifies the effects on selection pressures, and thus on the shapes of expected evolutionary trajectories. The second, an effective population size, quantifies the effects on selection responses, and thus on the expected rates of adaptation. Applying our results to two social dilemmas, we show how the range of evolutionarily stable cooperative behaviors systematically varies with a model's structure coefficient.2

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“…It is also possible that they play a variable number of games or even just one game in each round of game playing [17]. The agents that an agent plays with are determined by a play graph, which may be fully connected, sparse, or possibly dynamically determined for example in function of neighborhood relations between agents [3,16,17]. Over many rounds and many generations of agents some game playing strategies may become dominant; these are the evolutionarily stable strategies (ESS).…”

Section: Simulation Of Evolution Of Cooperationmentioning

confidence: 99%

“…More recent simulation studies considered the replacement of the fully connected graph by less connected interaction graphs, e.g. scale-free and small-world graphs [16] -note that in all these cases the interaction graph is given by design of the simulation. Another approach is to let the interaction graph be driven by spatial neighborhood arrangements, i.e.…”

Section: Introductionmentioning

confidence: 99%

Networks of Artificial Social Interactions

András

2011

Advances in Artificial Life. Darwin Meets Von Neumann

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Abstract. Evolution of cooperation is a fundamental question of socio-biology. Intrinsic factors like kinship play an important role in cooperation among selfish individuals. External factors like uncertainty and the structure of the social interaction network also contribute significantly to the evolution of cooperation. Here I use agent-based simulations to generate artificial social networks. I show that some of these networks have similar scale-free structure as real social networks. The analysis shows that having agents with memory and with the ability to share their memory through gossiping does not have a significant effect on the scale-free nature of simulated social networks. However the presence of high uncertainty in the cooperation games played by the agents is required for the generation of scale-free social interaction networks.

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Evolutionary stability on graphs

Cited by 112 publications

References 76 publications

One-third rules with equality: Second-order evolutionary stability conditions in finite populations

One-third rules with equality: Second-order evolutionary stability conditions in finite populations

Adaptive Dynamics with Interaction Structure

Networks of Artificial Social Interactions

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