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

## Author Info

• Sandholm, William H.

()
(Department of Economics, University of Wisconsin)

Registered author(s):

## 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 $\mu^{N,\eta}$ 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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20100001/3302/135

## Bibliographic Info

Article provided by Econometric Society in its journal Theoretical Economics.

Volume (Year): 5 (2010)
Issue (Month): 1 (January)
Pages:

as in new window
Handle: RePEc:the:publsh:554

Contact details of provider:
Web page: http://econtheory.org

## Related research

Keywords: Evolutionary game theory; stochastic stability; equilibrium selection;

Find related papers by JEL classification:

• C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
• C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

## References

No references listed on IDEAS
You can help add them by filling out this form.

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
1. Ryoji Sawa, 2012. "Mutation rates and equilibrium selection under stochastic evolutionary dynamics," International Journal of Game Theory, Springer, vol. 41(3), pages 489-496, August.
2. Sandholm, William H., 2012. "Stochastic imitative game dynamics with committed agents," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2056-2071.
3. Staudigl, Mathias, 2012. "Stochastic stability in asymmetric binary choice coordination games," Games and Economic Behavior, Elsevier, vol. 75(1), pages 372-401.
4. Robert Molzon, 2012. "Large Population Limits for Evolutionary Dynamics with Random Matching," Dynamic Games and Applications, Springer, vol. 2(1), pages 146-159, March.
5. Kevin Hasker, 2014. "The Emergent Seed: A Representation Theorem for Models of Stochastic Evolution and two formulas for Waiting Time," Levine's Working Paper Archive 786969000000000954, David K. Levine.

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

## Corrections

When requesting a correction, please mention this item's handle: RePEc:the:publsh:554. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Martin J. Osborne).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.