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T-Space at The University of Toronto Libraries >
Theoretical Economics >
Volume 5, Number 1 (January 2010) >

Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/18347

Title: Orders of limits for stationary distributions, stochastic dominance, and stochastic stability
Authors: William H. Sandholm; Department of Economics, University of Wisconsin
Keywords: Evolutionary game theory, stochastic stability, equilibrium selection
C72, C73
Issue Date: 26-Jan-2010
Publisher: Theoretical Economics
Citation: Theoretical Economics; Vol 5, No 1 (2010)
Abstract: [This item is a preserved copy. To view the original, visit http://econtheory.org/] 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 $\mu^{N,\eta}$ 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.
URI: http://hdl.handle.net/1807/18347
Other Identifiers: http://econtheory.org/ojs/index.php/te/article/view/20100001
Rights: Authors who publish in <i>Theoretical Economics</i> will release their articles under the <a href="http://creativecommons.org/licenses/by-nc/2.5/">Creative Commons Attribution-NonCommercial license</a>. This license allows anyone to copy and distribute the article for non-commercial purposes provided that appropriate attribution is given.
Appears in Collections:Volume 5, Number 1 (January 2010)

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