An Evolutionary Interpretation of Mixed-Strategy Equilibria
One of the more convincing interpretations of mixed strategy equilibria describes a mixed equilibrium as a steady state in a large population in which all players use pure strategies but the population as a whole mimics a mixed strategy. To be complete, however, this interpretation requires a good story about how the population arrives at the appropriate distribution over pure strategies. In this paper I attempt to give an explanation based on an evolutionary, stochastic learning process. Convergence properties of these processes have been studied extensively but almost exclusively for the case of convergence to pure Nash equilibria. Here I study the conditions under which an evolutionary process converges to population mixed-strategy equilibria. I find that not all mixed equilibria can be justified as the result of the evolutionary learning process even if the equilibrium is unique. For symmetric 2x2 and 3x3 games I give necessary and sufficient conditions for convergence and for n*n games I give a sufficient condition. For cases in which the conditions are not satisfied counterexamples are given, in which the process enters a limit cycle.
(This abstract was borrowed from another version of this item.)
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- repec:att:wimass:9122 is not listed on IDEAS
- Fudenberg, D. & Kreps, D.M., 1992.
"Learning Mixed Equilibria,"
92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
- James Bergin & B. L. Lipman, 1994.
"Evolution with state-dependent mutations,"
199411, School of Economics, University College Dublin.
- BERGIN, James & LIPMAN, Bart, 1994. "Evolution with State-Dependent Mutations," CORE Discussion Papers 1994055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- J. Bergin & B. Lipman, 2010. "Evolution with State-Dependent Mutations," Levine's Working Paper Archive 486, David K. Levine.
- J Bergin & B L Lipman, 1997. "Evolution with state-dependent Mutations," Levine's Working Paper Archive 771, David K. Levine.
- Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
- Ellison, Glenn, 1993.
"Learning, Local Interaction, and Coordination,"
Econometric Society, vol. 61(5), pages 1047-71, September.
- Ritzberger, Klaus & Weibull, Jorgen W, 1995.
"Evolutionary Selection in Normal-Form Games,"
Econometric Society, vol. 63(6), pages 1371-99, November.
- Crawford, Vincent P., 1985. "Learning behavior and mixed-strategy Nash equilibria," Journal of Economic Behavior & Organization, Elsevier, vol. 6(1), pages 69-78, March.
- Ariel Rubinstein, 1988. "Comments on the interpretation of game theory (Now published in Econometrica, 59 (1991), pp.909-924.)," STICERD - Theoretical Economics Paper Series 181, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Martin J Osborne & Ariel Rubinstein, 2009.
"A Course in Game Theory,"
814577000000000225, UCLA Department of Economics.
- Rosenthal, R W, 1979. "Sequences of Games with Varying Opponents," Econometrica, Econometric Society, vol. 47(6), pages 1353-66, November.
- Kandori, M. & Mailath, G.J., 1991.
"Learning, Mutation, And Long Run Equilibria In Games,"
71, Princeton, Woodrow Wilson School - John M. Olin Program.
- Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
- M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
- Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
- Kandori Michihiro & Rob Rafael, 1995.
"Evolution of Equilibria in the Long Run: A General Theory and Applications,"
Journal of Economic Theory,
Elsevier, vol. 65(2), pages 383-414, April.
- M. Kandori & R. Rob, 2010. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Levine's Working Paper Archive 502, David K. Levine.
- Robson, Arthur J. & Vega-Redondo, Fernando, 1996.
"Efficient Equilibrium Selection in Evolutionary Games with Random Matching,"
Journal of Economic Theory,
Elsevier, vol. 70(1), pages 65-92, July.
- Arthur J Robson & Fernando Vega-Redondo, 1999. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Levine's Working Paper Archive 2112, David K. Levine.
- Noldeke Georg & Samuelson Larry, 1993.
"An Evolutionary Analysis of Backward and Forward Induction,"
Games and Economic Behavior,
Elsevier, vol. 5(3), pages 425-454, July.
- Noeldecke,Georg & Samuelson,Larry, . "An evolutionary analysis of backward and forward induction," Discussion Paper Serie B 228, University of Bonn, Germany.
- G. Noldeke & L. Samuelson, 2010. "An Evolutionary Analysis of Backward and Forward Induction," Levine's Working Paper Archive 538, David K. Levine.
- Oechssler, Jorg, 1997.
"Decentralization and the coordination problem,"
Journal of Economic Behavior & Organization,
Elsevier, vol. 32(1), pages 119-135, January.
- Joerg Oechssler, 1993. "Competition among Conventions," Game Theory and Information 9312001, EconWPA, revised 04 Dec 1993.
When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:21:y:1997:i:1-2:p:203-237. 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: (Zhang, Lei)
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.