Game-Theoretical Models in Biology

Broom, Mark; Rychtář, Jan

doi:10.1201/b14069

Cited by 189 publications

(218 citation statements)

References 0 publications

Supporting

Mentioning

211

Contrasting

Unclassified

Order By: Relevance

“…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.

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

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

Sample

Allen

2017

J. Math. Biol.

View full text Add to dashboard Cite

show abstract

“…Besides our recent article (Garay et al 2017) that provides the foundation of the current investigation, Krivan and Cressman (2017) analyze general two-strategy matrix games when individuals are always paired, as in classical matrix games, but their interaction times depend on the strategies used in the pair. They were able to give an explicit formula for the stationary distribution for the standard polymorphic model in this case, in contrast to the implicit form we are forced to use in (2). On the other hand, our model extends theirs to include other activities beyond pair interactions that are essential to include for more realistic models of ecological systems.…”

Section: Discussionmentioning

confidence: 99%

“…For individual fitness in this game, we follow Garay et al (2017) who assume a continuous time Markov model is used where a focal individual's time between encounters when active and the amount of time it is inactive are independent and exponentially distributed with prescribed mean. 2 For a large population in this situation, they show that the fitness of the focal individual is given by the quotient…”

Section: Matrix Games Under Time Constraints and The Monomorphic Modelmentioning

confidence: 99%

“…For classical matrix games (i.e. matrix games without time constraints), these two concepts are connected by one part of the folk theorem of evolutionary game theory (Hofbauer and Sigmund, 1998;Cressman, 2003;Broom and Rychtar, 2013): An ESS is a locally asymptotically stable rest point of the replicator equation. The fundamental question of this paper is then: What is the connection between ESSs and stable rest points of the standard replicator equation in the class of matrix games under time constraints?…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The ESS and replicator equation in matrix games under time constraints

et al. 2018

View full text Add to dashboard Cite

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.

show abstract

“…The specific type that we consider, and the most commonly used, is multiplayer matrix games, which can be though of as a special type of the nonlinear games in Section 2, although we note that multiplayer games in general do not simply reduce to this type. The text in significant part follows a tutorial talk given by MB at the International Society on Dynamic Games Symposium in Amsterdam in July 2014, which in turn followed aspects of the book Broom and Rychtář (2013).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear and Multiplayer Evolutionary Games

Broom

Rychtář

2016

Advances in Dynamic and Evolutionary Games

Self Cite

View full text Add to dashboard Cite

This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract Classical evolutionary game theory has typically considered populations within which randomly selected pairs of individuals play games against each other, and the resulting payoff functions are linear. These simple functions have led to a number of pleasing results for the dynamic theory, the static theory of evolutionarily stable strategies, and the relationship between them. We discuss such games, together with a basic introduction to evolutionary game theory, in Section 1. Realistic populations, however, will generally not have these nice properties, and the payoffs will be nonlinear. In Section 2 we discuss various ways in which nonlinearity can appear in evolutionary games, including pairwise games with strategy-dependent interaction rates, and playing the field games, where payoffs depend upon the entire population composition, and not on individual games. In Section 3 we consider multiplayer games, where payoffs are the result of interactions between groups of size greater than two, which again leads to nonlinearity, and a breakdown of some of the classical results of Section 1. Finally in Section 4 we summarise and discuss the previous sections. Permanent repository link

show abstract

Game-Theoretical Models in Biology

Cited by 189 publications

References 0 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

The ESS and replicator equation in matrix games under time constraints

Nonlinear and Multiplayer Evolutionary Games

Contact Info

Product

Resources

About