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Evolutionary game theory

Evolutionary game theory (EGT) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith and George R. Price's formalisation of contests, analysed as strategies, and the mathematical criteria that can be used to predict the results of competing strategies.[1]

Evolutionary game theory differs from classical game theory in focusing more on the dynamics of strategy change.[2] This is influenced by the frequency of the competing strategies in the population.[3]


Evolutionary game theory has helped to explain the basis of altruistic behaviours in Darwinian evolution. It has in turn become of interest to economists,[4] sociologists, anthropologists, and philosophers.

If a hawk meets a dove, the hawk gets the full resource V

If a hawk meets a hawk, half the time they win, half the time they lose, so the average outcome is then V/2 minus C/2

If a dove meets a hawk, the dove will back off and get nothing – 0

If a dove meets a dove, both share the resource and get V/2

An optimal strategy: that would maximize fitness, and many ESS states are far below the maximum fitness achievable in a fitness landscape. (See hawk dove graph above as an example of this.)

A singular solution: often several ESS conditions can exist in a competitive situation. A particular contest might stabilize into any one of these possibilities, but later a major perturbation in conditions can move the solution into one of the alternative ESS states.

Always present: it is possible for there to be no ESS. An evolutionary game with no ESS is "rock-scissors-paper", as found in species such as the side-blotched lizard ().

Uta stansburiana

An unbeatable strategy: the ESS is only an uninvadeable strategy.

The orange throat is very aggressive and operates over a large territory – attempting to mate with numerous females

The unaggressive yellow throat mimics the markings and behavior of female lizards, and "sneakily" slips into the orange throat's territory to mate with the females there (thereby taking over the population)

The blue throat mates with, and carefully guards, one female – making it impossible for the sneakers to succeed and therefore overtakes their place in a population

Evolutionary games which lead to a stable situation or point of stasis for contending strategies which result in an evolutionarily stable strategy

Evolutionary games which exhibit a cyclic behaviour (as with RPS game) where the proportions of contending strategies continuously cycle over time within the overall population

Two types of dynamics:


A third, coevolutionary, dynamic, combines intra-specific and inter-specific competition. Examples include predator-prey competition and host-parasite co-evolution, as well as mutualism. Evolutionary game models have been created for pairwise and multi-species coevolutionary systems.[58] The general dynamic differs between competitive systems and mutualistic systems.


In competitive (non-mutualistic) inter-species coevolutionary system the species are involved in an arms race – where adaptations that are better at competing against the other species tend to be preserved. Both game payoffs and replicator dynamics reflect this. This leads to a Red Queen dynamic where the protagonists must "run as fast as they can to just stay in one place".[59]


A number of evolutionary game theory models have been produced to encompass coevolutionary situations. A key factor applicable in these coevolutionary systems is the continuous adaptation of strategy in such arms races. Coevolutionary modelling therefore often includes genetic algorithms to reflect mutational effects, while computers simulate the dynamics of the overall coevolutionary game. The resulting dynamics are studied as various parameters are modified. Because several variables are simultaneously at play, solutions become the province of multi-variable optimisation. The mathematical criteria of determining stable points are Pareto efficiency and Pareto dominance, a measure of solution optimality peaks in multivariable systems.[60]


Carl Bergstrom and Michael Lachmann apply evolutionary game theory to the division of benefits in mutualistic interactions between organisms. Darwinian assumptions about fitness are modeled using replicator dynamics to show that the organism evolving at a slower rate in a mutualistic relationship gains a disproportionately high share of the benefits or payoffs.[61]

Davis, Morton; "Game Theory – A Nontechnical Introduction", Dover Books,  0-486-29672-5

ISBN

(2006). The Selfish Gene (30th anniversary ed.). Oxford: Oxford University Press. ISBN 978-0-19-929115-1.

Dawkins, Richard

Dugatkin and Reeve; "Game Theory and Animal Behavior", Oxford University Press,  0-19-513790-6

ISBN

Hofbauer and Sigmund; "Evolutionary Games and Population Dynamics", Cambridge University Press,  0-521-62570-X

ISBN

Kohn, Marek; "A Reason for Everything", Faber and Faber,  0-571-22393-1

ISBN

Li Richter and Lehtonen (Eds.) "Half a century of evolutionary games: a synthesis of theory, application and future directions", Philosophical Transactions of the Royal Society B,

Volume 378, Issue 1876

Sandholm, William H.; "Population Games and Evolutionary Dynamics", The MIT Press,  0262195879

ISBN

Segerstrale, Ullica; "Nature's Oracle – The life and work of W.D. Hamilton", Oxford University Press, 2013,  978-0-19-860727-4

ISBN

; "Games of Life", Penguin Books, also Oxford University Press, 1993, ISBN 0198547838

Sigmund, Karl

Vincent and Brown; "Evolutionary Game Theory, Natural Selection and Darwinian Dynamics", Cambridge University Press,  0-521-84170-4

ISBN

Theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions' (2023)

Evolutionary game theory at the Stanford Encyclopedia of Philosophy

Evolving Artificial Moral Ecologies at The Centre for Applied Ethics, University of British Columbia

at Curlie

Evolutionary game theory

. Web of Stories. 1997 – via YouTube. (via Web of Stories)

"Life and work of John Maynard Smith, interviewed by Richard Dawkins"