2010
DOI: 10.3982/te554
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Orders of limits for stationary distributions, stochastic dominance, and stochastic stability

Abstract: A population of agents recurrently plays a two-strategy population game. When an agent receives a revision opportunity, he chooses a new strategy using a noisy best response rule that satisfies mild regularity conditions; best response with mutations, logit choice, and probit choice are all permitted. We study the long run behavior of the resulting Markov process when the noise level η is small and the population size N is large. We obtain a precise characterization of the asymptotics of the stationary distrib… Show more

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Cited by 37 publications
(6 citation statements)
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“…The definition of c 1 xy (∞), however, implies that for all sufficiently large n and sufficiently small ε, Recall Eq. ( 7) and (19). The above observation suggests that T * xy (∞) = B 1 y (∞).…”
mentioning
confidence: 71%
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“…The definition of c 1 xy (∞), however, implies that for all sufficiently large n and sufficiently small ε, Recall Eq. ( 7) and (19). The above observation suggests that T * xy (∞) = B 1 y (∞).…”
mentioning
confidence: 71%
“…The double-limit approach, though convincing, revealed a new issue; the equilibrium selection result may depend on the order of limits. [19] addresses this issue and shows that for two-strategy games, the selection result coincides among both orders of limits under noisy best response choice rules.…”
mentioning
confidence: 97%
“…In this section, we consider evolution in two-strategy games under a general class of perturbed best response protocols (see Example 4) which includes the logit and probit choice rules. This section is based on [42].…”
Section: Proof (I) This Follows From (Iii)mentioning
confidence: 99%
“…Large population double limit (LPDL; N → ∞ and then η → 0): This limit is largely unexplored. The only reported results in this limit case are in [42].…”
mentioning
confidence: 90%
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