Exit from equilibrium in coordination games under probit choice

Stochastic stability in the large population and small mutation limits for coordination games

“…For the large population limit, however, games are usually restricted to two strategies. 1 The technique of [7] often used in stochastic stability analysis cannot be directly applied due to that the state space of the process depends on the population size. For two-strategy games, the process can be reduced to a birth-and-death process, which is amenable to calculations of the stationary distribution (see [21,22] for example).…”

“…Though our model differs from theirs, we provide an answer to the question. [9,24,25,1,2] study stochastic stability in the double limit in general normal form games. [9] Figure 1.…”

“…In the same issue of this journal, [30] reports the recent development along the line of research of [24,25]. By resorting to the technique developed by [26], [1,2] examine stochastically stable states in the double limit for a class of more-than-two-strategy games. [1] considers three-strategy coordination games under the probit dynamics; [2] considers bilingual games under the logit dynamics.…”

“…By resorting to the technique developed by [26], [1,2] examine stochastically stable states in the double limit for a class of more-than-two-strategy games. [1] considers three-strategy coordination games under the probit dynamics; [2] considers bilingual games under the logit dynamics. Our difference from [24,25,1,2] is the specification of the timing of agents' updates.…”

“…[1] considers three-strategy coordination games under the probit dynamics; [2] considers bilingual games under the logit dynamics. Our difference from [24,25,1,2] is the specification of the timing of agents' updates. We employ synchronous update, in which all agents update in each period, while they employ asynchronous update, in which one agent updates in each period.…”