Stochastically stable equilibrium
Encyclopedia
In game theory
, a stochastically stable equilibrium is a refinement
of the evolutionarily stable state
in evolutionary game theory
, proposed by Dean Foster and Peyton Young
. 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 mutation
). 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
.
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
, a stochastically stable equilibrium is a refinement
Solution concept
In game theory, a solution concept is a formal rule for predicting how the game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players, therefore predicting the result of the game...
of the evolutionarily stable state
Evolutionarily stable state
"A population is said to be in an evolutionarily stable state if its genetic composition is restored by selection after a disturbance, provided the disturbance is not too large...
in evolutionary game theory
Evolutionary game theory
Evolutionary game theory is the application of Game Theory to evolving populations of lifeforms in biology. EGT is useful in this context by defining a framework of contests, strategies and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith...
, proposed by Dean Foster and Peyton Young
Peyton Young
Hobart Peyton Young is an American game theorist 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 learning in games...
. 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 mutation
Mutation
In molecular biology and genetics, mutations are changes in a genomic sequence: the DNA sequence of a cell's genome or the DNA or RNA sequence of a virus. They can be defined as sudden and spontaneous changes in the cell. Mutations are caused by radiation, viruses, transposons and mutagenic...
). 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
*In linguistics, the potential mood*The mathematical study of potentials is known as potential theory; it is the study of harmonic functions on manifolds...
.