Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/150130
Title:

# Orders of limits for stationary distributions, stochastic dominance, and stochastic stability

Authors:
Sandholm, William H.
Year of Publication:
2010
Citation:
[Journal:] Theoretical Economics [ISSN:] 1555-7561 [Volume:] 5 [Year:] 2010 [Issue:] 1 [Pages:] 1-26
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 $\eta$ is small and the population size $N$ is large. We obtain a precise characterization of the asymptotics of the stationary distributions $\muN,\eta}$ as $\eta$ approaches zero and $N$ approaches infinity, and we establish that these asymptotics are the same for either order of limits and for all simultaneous limits. In general, different noisy best response rules can generate different stochastically stable states. To obtain a robust selection result, we introduce a refinement of risk dominance called \emph{stochastic dominance}, and we prove that coordination on a given strategy is stochastically stable under every noisy best response rule if and only if that strategy is stochastically dominant.
Subjects:
Evolutionary game theory
stochastic stability
equilibrium selection
JEL:
C72
C73
Persistent Identifier of the first edition:
Document Type:
Article
Appears in Collections:

Files in This Item:
File
Size
277.86 kB