Evolutionary stable strategies and game dynamics

Taylor, Peter; Jonker, Leo

doi:10.1016/0025-5564(78)90077-9

Cited by 2,844 publications

(1,819 citation statements)

References 3 publications

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“…In a well-mixed population, the expected payoff of strategy i is calculated as f i = j f ij x j . The replicator equation [42,43,44] then describes the time evolution of x i in the following way: where the left-hand side means the time derivative of x i and f ≡ j f j x j = ij f ij x i x j is the mean payoff of the population. The last term on the righthand side describes mutation with rate µ, which is set to be 10 −4 in our numerical calculation.…”

Section: Evolutionary Dynamicsmentioning

confidence: 99%

Combination with anti-tit-for-tat remedies problems of tit-for-tat

Baek

Choi

2017

Journal of Theoretical Biology

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One of the most important questions in game theory concerns how mutual cooperation can be achieved and maintained in a social dilemma. In Axelrod's tournaments of the iterated prisoner's dilemma, Tit-for-Tat (TFT) demonstrated the role of reciprocity in the emergence of cooperation. However, the stability of TFT does not hold in the presence of implementation error, and a TFT population is prone to neutral drift to unconditional cooperation, which eventually invites defectors. We argue that a combination of TFT and anti-TFT (ATFT) overcomes these difficulties in a noisy environment, provided that ATFT is defined as choosing the opposite to the opponent's last move. According to this TFT-ATFT strategy, a player normally uses TFT; turns to ATFT upon recognizing his or her own error; returns to TFT either when mutual cooperation is recovered or when the opponent unilaterally defects twice in a row. The proposed strategy provides simple and deterministic behavioral rules for correcting implementation error in a way that cannot be exploited by the opponent, and suppresses the neutral drift to unconditional cooperation.

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Section: Evolutionary Dynamicsmentioning

confidence: 99%

Combination with anti-tit-for-tat remedies problems of tit-for-tat

Baek

Choi

2017

Journal of Theoretical Biology

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“…The mathematical foundation of evolutionary game dynamics is the replicator equation (Taylor and Jonker, 1978;Hofbauer et al, 1979;Zeeman, 1980), which is a system of ordinary differential equations describing how the relative abundances (frequencies) of strategies change over time as a consequence of frequency dependent selection. The payoff from the game is interpreted as biological fitness.…”

Section: Introductionmentioning

confidence: 99%

Active linking in evolutionary games

Pacheco

Traulsen

Nowak

2006

Journal of Theoretical Biology

236

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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“…For instance, under the replicator equation (Taylor and Jonker 1978) of the standard polymorphic population model (i.e. each phenotype existing in the population is a pure strategy), the evolutionary outcome is characterized as a locally asymptotically stable rest point of this dynamical system.…”

Section: Introductionmentioning

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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Evolutionary stable strategies and game dynamics

Cited by 2,844 publications

References 3 publications

Combination with anti-tit-for-tat remedies problems of tit-for-tat

Combination with anti-tit-for-tat remedies problems of tit-for-tat

Active linking in evolutionary games

The ESS and replicator equation in matrix games under time constraints

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