Interaction times change evolutionary outcomes: Two-player matrix games

Křivan, Vlastimil; Cressman, Ross

doi:10.1016/j.jtbi.2017.01.010

Cited by 27 publications

(63 citation statements)

References 13 publications

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“…Moreover, at certain time delays, the interior stationary state ceases to exist or 181 there may appear another interior stationary state. Our results are qualitatively similar 182 to those obtained in [14] in a completely different model. We considered only a special 183 case study, more systematic investigations are needed, especially concerning classic 184 games describing social dilemmas.…”

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confidence: 79%

Evolution of populations with strategy-dependent time delays

Miękisz

Bodnar

2019

Preprint

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We address the issue of stability of coexistence of two strategies with respect to time delays in evolving populations. It is well known that time delays may cause oscillations. Here we report a novel behavior. We show that a microscopic model of evolutionary games with a unique mixed evolutionarily stable strategy (a globally asymptotically stable interior stationary state in the standard replicator dynamics) and with strategy-dependent time delays leads to a new type of replicator dynamics. It describes the time evolution of fractions of the population playing given strategies and the size of the population. Unlike in all previous models, an interior stationary state of such dynamics depends continuously on time delays and at some point it might disappear, no cycles are present. In particular, this means that an arbitrarily small time delay changes an interior stationary state. Moreover, at certain time delays, there may appear another interior stationary state. Author summarySocial and biological processes are usually described by ordinary or partial differential 1 equations, or by Markov processes if we take into account stochastic perturbations. 2 However, interactions between individuals, players or molecules, naturally take time. 3Results of biological interactions between individuals may appear in the future, and in 4 social models, individuals or players may act, that is choose appropriate strategies, on 5 the basis of the information concerning events in the past. It is natural therefore to 6 introduce time delays into evolutionary game models. It was usually observed, and 7 expected, that small time delays do not change the behavior of the system and large 8 time delays may cause oscillations. Here we report a novel behavior. We show that 9 microscopic models of evolutionary games with strategy-dependent time delays, in 10 which payoffs appear some time after interactions of individuals, lead to a new type of 11 replicator dynamics. Unlike in all previous models, interior stationary states of such 12 dynamics depend continuously on time delays. This shows that effects of time delays 13 are much more complex than it was previously thought. 14 Introduction 15Many social and biological processes can be modeled as systems of interacting 16 individuals within the framework of evolutionary game theory [9, 11, 15-17, 22, 23, 26, 29]. 17 The evolution of very large (infinite) populations can be then given by differential 18 the basis of the information concerning events in the past. It is natural therefore to 25 introduce time delays into evolutionary game models. 26It is well known that time delays may cause oscillations in dynamical systems [2][3][4][5]. 27 One usually expects that interior equilibria of evolving populations, describing 28 coexisting strategies or behaviors, are asymptotically stable for small time delays and 29 above a critical time delay, where the Hopf bifurcation appears, they become unstable, 30 evolutionary dynamics exhibits oscillations and cycles. Here we report a novel behavior -31 ...

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confidence: 79%

Evolution of populations with strategy-dependent time delays

Miękisz

Bodnar

2019

Preprint

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“…They also use Markov processes to describe the stationary state of the predator population (Broom et al 2010, Yates andBroom 2007). The second research line concerns matrix games under time constraint, where the stage differential equations are also used to find the steady state of the players Krivan 2019, Krivan andCressman 2017), moreover, the Markov processes are also applied to describe the stationary state of the players (Garay et al 2016). Based on all this, I hope the derivation methods overviewed here will be useful not only in ecology, but also in evolutionary game theory when the time constraints take place.…”

Section: Discussionmentioning

confidence: 99%

“…The adaptive dynamics approach as an evolutionary research line also uses this functional response derivation method in model building (Dercole 2016). I note that this deterministic mass action method is widely used in evolutionary game theory under time constraint Rychtar 2013, Krivan andCressman 2017) as well.…”

Section: Functional Responsesmentioning

confidence: 99%

Technical review on derivation methods for behavior dependent functional responses

Garay

2019

Community Ecology

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“…13 The effect of time constraints on evolutionary outcomes has been studied elsewhere in the literature. 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).…”

Section: Discussionmentioning

confidence: 99%

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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Interaction times change evolutionary outcomes: Two-player matrix games

Cited by 27 publications

References 13 publications

Evolution of populations with strategy-dependent time delays

Evolution of populations with strategy-dependent time delays

Technical review on derivation methods for behavior dependent functional responses

The ESS and replicator equation in matrix games under time constraints

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