Strategy abundance in games for arbitrary mutation rates

Antal, Tibor; Nowak, Martin A.; Traulsen, Arne

doi:10.1016/j.jtbi.2008.11.023

Cited by 91 publications

(85 citation statements)

References 24 publications

(51 reference statements)

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“…Nevertheless, in evolutionary and ecological situations there is not only the reproductive rate but also the carrying capacity [21]. The density-dependent dynamic system became a very important direction in evolutionary research [1,2,4]. In order to combine the payoff matrix with competitive Lotka-Volterra equations, Sebastian presented the density game [21].…”

Section: Symbiosis Model On Green Building With Considering Payofmentioning

confidence: 99%

“…Equilibrium stability analysis of equation (1) should be developed in order to explore the symbiotic evolution characteristics of different agents shown in equation (1). According to the stability theory of ordinary differential equations, the equation (1) …”

Section: Stability Analysis Of the Model 1) Equilibrium Stability mentioning

confidence: 99%

“…Starting form this region, the phase point tends to be stable at or enters into area or area . of two agents, and the influence of the model parameters on the stability point is discussed according equation (1). Equation (6) to (10) …”

Section: Stability Analysis Of the Model 1) Equilibrium Stability mentioning

confidence: 99%

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Density game analysis and evolutionary equilibrium of supply side symbiosis behavior of green building considering the market carrying capacity

Huang

2017

2017 2nd International Conference on Knowledge Engineering and Applications (ICKEA)

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obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The WestminsterResearch online digital archive at the University of Westminster aims to make the research output of the University available to a wider audience. Copyright and Moral Rights remain with the authors and/or copyright owners.Whilst further distribution of specific materials from within this archive is forbidden, you may freely distribute the URL of WestminsterResearch: ((http://westminsterresearch.wmin.ac.uk/).In case of abuse or copyright appearing without permission e-mail repository@westminster.ac.uk Huang, Dingxuan & Li, Shuliang. "Density Game Analysis and Evolutionary Equilibrium of Supply Side Symbiosis Behavior of Green Building Considering the Market Carrying Capacity", Proceedings of the 2nd International Conference on Knowledge Engineering and Applications (ICKEA2017), 21 st to 23rd October 2017, Imperial College London, UK. IEEE. Density Game Analysis and Evolutionary Equilibrium of Supply Side SymbiosisBehavior of Green Building Considering the Market Carrying Capacity Abstract-The process of green building development involves not only the symbiotic changes on the numbers of green and traditional buildings, but also the game payment of the agents. According to the symbiosis theory and evolutionary game theory, a symbiosis model of green building supply side is established, with the construction market carrying capacity considered. The evolutionary stable points and stability conditions of the symbiotic evolutionary model are analyzed and discussed. The results show that the stable condition of the symbiotic evolution between different agents in proposed symbiosis model depends upon the combination of the game payment of different agents, but has nothing to do with the reproduction rate. It is also shown that relaxing the cap on the upper limit or maximum volume of the construction market will lead to both the numbers of green buildings and the numbers of government incentives increase at the same time.

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Section: Symbiosis Model On Green Building With Considering Payofmentioning

confidence: 99%

Section: Stability Analysis Of the Model 1) Equilibrium Stability mentioning

confidence: 99%

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Density game analysis and evolutionary equilibrium of supply side symbiosis behavior of green building considering the market carrying capacity

Huang

2017

2017 2nd International Conference on Knowledge Engineering and Applications (ICKEA)

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“…Stationary distributions for the Moran process in two dimensions and some recently-studied generalizations are given in several recent works [1,36,[46][47][48][49][50]; stationary distributions for both the Moran process and the Wright-Fisher process have been studied in [51]; a number of formulas for various finite population processes are given in [52] and [53]. The n = 2 solution only relies on the fact that the transition matrix is tridiagonal, and so applies to the incentive process with mutation without modification.…”

Section: Stationary Distributionsmentioning

confidence: 99%

Stationary Stability for Evolutionary Dynamics in Finite Populations

Harper¹,

Fryer

2016

Entropy

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Abstract:We demonstrate a vast expansion of the theory of evolutionary stability to finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability. We define the notion of stationary stability for the Moran process with mutation and generalizations, as well as a generalized notion of evolutionary stability that includes mutation called an incentive stable state (ISS) candidate. For sufficiently large populations, extrema of the stationary distribution are ISS candidates and we give a family of Lyapunov quantities that are locally minimized at the stationary extrema and at ISS candidates. In various examples, including for the Moran and Wright-Fisher processes, we show that the local maxima of the stationary distribution capture the traditionally-defined evolutionarily stable states. The classical stability theory of the replicator dynamic is recovered in the large population limit. Finally we include descriptions of possible extensions to populations of variable size and populations evolving on graphs.

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“…Some of the corresponding methods require weak selection or rare mutations. But analytical results are also available when selection is strong [14], mutation rates are arbitrary [15,16], or when more than two players are involved in any particular interaction [17,18]. Even the evolution in continuous strategy spaces can be captured with simple differential equations, using the framework of adaptive dynamics in infinite [19] or finite populations [20].…”

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confidence: 99%