Testing Game Theory

Weibull, Jörgen W.

doi:10.1057/9780230523371_6

Cited by 250 publications

(305 citation statements)

References 39 publications

(49 reference statements)

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“…Evolutionary game theory (Maynard Smith, 1982;Maynard Smith and Price, 1973;Hofbauer and Sigmund, 1998;Weibull, 1997;Broom and Rychtár, 2013) is a framework for modeling the evolution of behaviors that affect others. Interactions are represented as a game, and game payoffs are linked to reproductive success.…”

Section: Introductionmentioning

confidence: 99%

The limits of weak selection and large population size in evolutionary game theory

Sample

Allen

2017

J. Math. Biol.

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Evolutionary game theory is a mathematical approach to studying how social behaviors evolve. In many recent works, evolutionary competition between strategies is modeled as a stochastic process in a finite population. In this context, two limits are both mathematically convenient and biologically relevant: weak selection and large population size. These limits can be combined in different ways, leading to potentially different results. We consider two orderings: the wN limit, in which weak selection is applied before the large population limit, and the N w limit, in which the order is reversed. Formal mathematical definitions of the N w and wN limits are provided. Applying these definitions to the Moran process of evolutionary game theory, we obtain asymptotic expressions for fixation probability and conditions for success in these limits. We find that the asymptotic expressions for fixation probability, and the conditions for a strategy to be favored over a neutral mutation, are different in the N w and wN limits. However, the ordering of limits does not affect the conditions for one strategy to be favored over another.

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Section: Introductionmentioning

confidence: 99%

The limits of weak selection and large population size in evolutionary game theory

Sample

Allen

2017

J. Math. Biol.

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“…The expected payoff of an individual is a linear function of the frequencies of all strategies; the coefficients of this function are the entries of the payoff matrix. For detailed reviews of the replicator equation and other approaches to evolutionary game dynamics, see Fudenberg and Tirole (1991), Weibull (1995), Samuelson (1997), Cressman (2003), Sigmund (1998, 2003), Gintis (2000) and Nowak and Sigmund (2004). in finite populations Imhof and Nowak, 2006;Taylor et al, 2004;Fudenberg et al, 2006;Traulsen et al, 2006a,b), in spatially extended systems (Nowak and May, 1992;Nakamaru et al, 1998;Killingback and Doebeli, 1996;van Baalen and Rand, 1998;Irwin and Taylor, 2001;Hauert and Doebeli, 2004;Ifti et al, 2004;Nakamaru and Iwasa, 2005;Jansen and van Baalen, 2006) or on graphs (Lieberman et al, 2005;Santos et al, , 2006a.…”

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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“…One of the core results in evolutionary game theory is that every evolutionarily stable strategy is locally asymptotically stable in the replicator dynamics Jonker, 1978, Hofbauer et al 1979; for more general accounts of evolutionary game theory see, for example, Weibull 1995, Hofbauer and Sigmund, 1998, Hofbauer and Sigmund, 2003, or Cressman 2003.…”

Section: Introductionmentioning

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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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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Testing Game Theory

Cited by 250 publications

References 39 publications

The limits of weak selection and large population size in evolutionary game theory

The limits of weak selection and large population size in evolutionary game theory

Active linking in evolutionary games

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

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