Evolution and the Theory of Games

Smith, John Maynard

doi:10.1007/978-1-4684-7862-4_22

Cited by 2,396 publications

(1,313 citation statements)

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“…Nash equilibrium is supposed to be a result of decisions of rational players. John Maynard Smith (1974Smith ( , 1982 has refined this concept of equilibrium to include the stability of Nash equilibria against mutants. He introduced the fundamental notion of an evolutionarily stable strategy.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium selection in evolutionary games with random matching of players

̧kisz

2005

Journal of Theoretical Biology

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We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant one, where players are averse to risks. We assume that individuals play with randomly chosen opponents (they do not play against average strategies as in the standard replicator dynamics). We show that the long-run behavior of a population depends on its size and the mutation level.

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Section: Introductionmentioning

confidence: 99%

Equilibrium selection in evolutionary games with random matching of players

̧kisz

2005

Journal of Theoretical Biology

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“…Eriksson et al 2004), and dispersal-foraging game (Garay et al 2015a). 3 Observe that the Holling functional response are defined in a similar way (Holling For the monomorphic model, we follow the setup of Maynard Smith (1982). That is, the resident population is monomorphic whereby every individual has resident phenotype p * .…”

Section: Matrix Games Under Time Constraints and The Monomorphic Modelmentioning

confidence: 99%

“…From the monomorphic approach of Maynard Smith (1982), we have the following definition (see also Garay et al (2017)). …”

Section: Matrix Games Under Time Constraints and The Monomorphic Modelmentioning

confidence: 99%

“…This theory is briefly summarized in Section 2 below by following the static ESS approach of Maynard Smith (1982). This approach assumes that there are only two phenotypes in the population at a given time, one of which is the fixed phenotype of the resident population and the other is a rare mutant phenotype.…”

Section: Introductionmentioning

confidence: 99%

“…Maynard Smith 1982, Garay et al 2017). Although the static ESS concept relies implicitly upon an underlying dynamic (see Maynard Smith (1982) as well as the discussion following Definition 2.1 below), its basic intuition concentrates on the evolutionary question: What phenotype is uninvadable by an arbitrary rare mutant?…”

Section: Introductionmentioning

confidence: 99%

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The ESS and replicator equation in matrix games under time constraints

et al. 2018

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Recently, we introduced the class of matrix games under time constraints and characterized the concept of (monomorphic) evolutionarily stable strategy (ESS) in them. We are now interested in how the ESS is related to the existence and stability of equilibria for polymorphic populations. We point out that, although the ESS may no longer be a polymorphic equilibrium, there is a connection between them. Specifically, the polymorphic state at which the average strategy of the active individuals in the population is equal to the ESS is an equilibrium of the polymorphic model.Moreover, in the case when there are only two pure strategies, a polymorphic equilibrium is locally asymptotically stable under the replicator equation for the pure-strategy polymorphic model if and only if it corresponds to an ESS. Finally, we prove that a strict Nash equilibrium is a pure-strategy ESS that is a locally asymptotically stable equilibrium of the replicator equation in n-strategy time-constrained matrix games.

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Finding Optimal Behaviors with Genetic Algorithms

Hoffmeister¹,

Wajnberg²

2008

Behavioral Ecology of Insect Parasitoids

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Optimality models used in behavioral ecology, and especially on insect parasitoids, have taken a variety of approaches, from classical analytical tools to individualbased simulations. The increasing awareness that much of the observable behavior in parasitoids depends on the state of the insect (be it the physiological or informational state) has led to the increasing use of stochastic dynamic programming models. However, optimal behaviors of one individual often depend upon the behavior of conspecifics, further complicating the issue. While classical game theory may be applied when behavior is not state dependent, genetic algorithms (GA) provide a powerful way in finding optimal behaviors for situations where such optimal behavior depends upon an animal's state and on the frequency of alternative behaviors of conspecifics. More generally, GAs can be used when there is a need to find the optimal strategy among a number of different alternative behaviors whose number is far too great to be exhaustively checked. GAs are search algorithms that proceed in a fashion analogous to natural selection. They are individual-based simulations that identify optimal solutions by searching the enormous space of potential solutions mimicking the process of evolution in biological systems.In this chapter, we discuss research questions in parasitoid behavioral ecology that might benefit from applying GA as a research tool for optimality models. Examples will be developed and explained. Among others, using the foraging problem of estimating habitat quality, we show how fast GAs find optimal solutions for parameter spaces that are impossible to solve numerically otherwise.

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Evolution and the Theory of Games

Cited by 2,396 publications

References 4 publications

Equilibrium selection in evolutionary games with random matching of players

Equilibrium selection in evolutionary games with random matching of players

The ESS and replicator equation in matrix games under time constraints

Finding Optimal Behaviors with Genetic Algorithms

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