Evolutionary Game Theory

Abstract

In the natural world, there is a constant struggle between individuals to survive and reproduce; for example, prey compete against their predators and conspecifics compete for resources such as food and territory. The outcomes of these conflicts depend on the strategies adopted by individuals and impact on reproductive success. The theory of evolutionary games, or evolutionary conflicts, addresses the issues of what strategies prevail and coexistence within these competitions under natural selection. The original models were based on competitions between identical conspecifics, although they now cover a huge range of complex behavioural scenarios such as the adoption of elaborate behaviours or costly physical ornaments by male animals seeking mates or the formation of dominance hierarchies among social groups.

Key Concepts:

  • Strategies are the possible behaviours open to an individual within a game.

  • Knowing the behaviour of each individual determines the rewards (payoffs) to all individuals in the game.

  • An evolutionarily stable strategy (ESS) is a strategy that, if played by almost all, resists invasion by any other strategy and so persists through time.

  • It is possible to have a single ESS, more than one ESS or no ESSs for a given game.

  • There is the potential for larger payoffs than under an ESS if individuals could co‐operate, but such strategies do not resist invasion and so are unstable.

  • While there may be more than one ESS, there are important restrictions on which can coexist for simple two‐player conflicts. More complex restrictions apply for multiplayer conflicts, and some of the simpler restrictions of the two‐player conflicts may not apply.

  • A population composed of individuals playing different strategies is subject to change following evolutionary dynamics, for example, replicator dynamics.

  • The rest points of evolutionary dynamics are not always the same as the ESSs of a conflict and care must be taken in any specific analysis.

  • If populations are subject to only small changes in strategy through mutation, change can be modelled by adaptive dynamics.

Keywords: strategy; conflict; evolution; stability; dynamics

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Further Reading

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Mesterton‐Gibbons M (1992) An Introduction to Game‐theoretic Modelling. New York: Addison‐Wesley.

Weibull JW (1995) Evolutionary Game Theory. Cambridge, MA: Massachusetts Institute of Technology Press.

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Broom, Mark, and Cannings, Chris(Nov 2010) Evolutionary Game Theory. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0005457.pub2]