# Evolutionarily Stable Strategies and Game Dynamics

@article{Taylor1978EvolutionarilySS, title={Evolutionarily Stable Strategies and Game Dynamics}, author={Peter D. Taylor and Leo B. Jonker}, journal={Bellman Prize in Mathematical Biosciences}, year={1978}, volume={40}, pages={145-156} }

We consider a class of matrix games in which successful strategies are rewarded by high reproductive rates, so become more likely to participate in subsequent playings of the game. Thus, over time, the strategy mix should evolve to some type of optimal or stable state. Maynard Smith and Price (1973) have introduced the concept of ESS (evolutionarily stable strategy) to describe a stable state of the game. We attempt to model the dynamics of the game both in the continuous case, with a system of… Expand

#### 2,236 Citations

Transition matrix model for evolutionary game dynamics.

- Mathematics, Medicine
- Physical review. E
- 2016

An evolutionary game model based on a transition matrix approach, in which the total change in the proportion of a population playing a given strategy is summed directly over contributions from all other strategies, which yields an endemic population playing non-Nash-equilibrium strategies. Expand

Stochastic stability in three-player games

- Mathematics, Biology
- Bulletin of mathematical biology
- 2005

The stochastic stability of equilibria in games with multiple evolutionarily stable strategies is analyzed and it is shown that, in some games, a population may not evolve in the long run to an evolutionarilystable equilibrium. Expand

Stable Population Games and Integrability for Evolutionary Dynamics∗

- 2008

We introduce a new class of population games called stable games. These games are characterized by self-defeating externalities: when agents revise their strategies, the improvements in the payoffs… Expand

Stability of evolutionarily stable strategies in discrete replicator dynamics with time delay.

- Mathematics, Medicine
- Journal of theoretical biology
- 2004

Two models of discrete-time replicator dynamics with time delay are constructed and it is shown that evolutionarily stable strategy is asymptotically stable for small time delays and becomes unstable for big ones when the population oscillates around its stationary state. Expand

ESS, population games, replicator dynamics: dynamics and games if not dynamic games

- Mathematics
- 2011

We review some classical definitions and results concerning Evolutionarily Stable Strategies (E.S.S.) with special emphasis on their link to Wardrop equilibrium, and on the nonlinear case where the… Expand

Evolutionary Game Theory and Evolutionary Stability

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- 2011

Evolutionary game theory is used to predict the behavior of individuals in populations (either of humans or other species) without relying on a detailed description of how these behaviors evolve over… Expand

Stable games and their dynamics

- Mathematics, Computer Science
- J. Econ. Theory
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It is proved that the set of Nash equilibria of a stable game is globally asymptotically stable under a wide range of evolutionary dynamics. Expand

Evolutionary game dynamics

- Mathematics
- 2011

Evolutionary game dynamics is the application of population dynamical methods to game theory. It has been introduced by evolutionary biologists, anticipated in part by classical game theorists. In… Expand

Population dynamics with a stable efficient equilibrium.

- Medicine, Biology
- Journal of theoretical biology
- 2005

It is shown that for a large range of parameters of dynamics, even if the initial conditions in both habitats are in the basin of attraction of the risk-dominant equilibrium (with respect to the standard replication dynamics without migration), in the long run most individuals play the efficient strategy. Expand

Stable Games

- Mathematics, Computer Science
- 2007 46th IEEE Conference on Decision and Control
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It is proved that the set of Nash equilibria of any stable game is convex and globally asymptotically stable under various classes of evolutionary dynamics, classes that include the best response dynamic, the Brown-von Neumann-Nash dynamic, and the Smith dynamic. Expand

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