In game theory, a stochastically stable equilibrium is a refinement of the

evolutionarily stable state A population can be described as being in an evolutionarily stable state when that population's "genetic composition is restored by selection after a disturbance, provided the disturbance is not too large" (Maynard Smith, 1982).Maynard Smith, J.. (1 ...

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 M ...

, proposed by

Dean Foster Dean may refer to: People * Dean (given name) * Dean (surname), a surname of Anglo-Saxon English origin * Dean (South Korean singer), a stage name for singer Kwon Hyuk * Dean Delannoit, a Belgian singer most known by the mononym Dean Titles * ...

and

Peyton Young Hobart Peyton Young (born March 9, 1945) is an American game theorist and economist known for his contributions to evolutionary game theory and its application to the study of institutional and technological change, as well as the theory of learn ...

. An evolutionary stable state S is also stochastically stable if under vanishing noise, the probability that the population is in the vicinity of state S does not go to zero. The concept is extensively used in models of learning in populations, where "noise" is used to model experimentation or replacement of unsuccessful players with new players (

random In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual ra ...

mutation In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA replication, DNA or viral repl ...

). Over time, as the need for experimentation dies down or the population becomes stable, the population will converge towards a subset of evolutionarily stable states. Foster and Young have shown that this subset is the set of states with the highest

potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple r ...

References

* Dean P. Foster and H. Peyton Young: "Stochastic Evolutionary Game Dynamics", ''Theoretical Population Biology'' 38(2), pp. 219–232(1990
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Game theory equilibrium concepts Evolutionary game theory {{gametheory-stub