IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Stochastic Adaptation in Finite Games Played by Heterogeneous Populations

  • Josephson, Jens

    ()

    (Dept. of Economics, Stockholm School of Economics)

In this paper, I analyze stochastic adaptation in finite n-player games played by heterogeneous populations of myopic best repliers, better repliers and imitators. In each period, one individual from each of n populations, one for each player role, is drawn to play and chooses a pure strategy according to her personal learning rule after observing a sample from a finite history. With a small probability individuals also make a mistake and play a pure strategy at random. I prove that, for a sufficiently low ratio between the sample and history size, only pure-strategy profiles in certain minimal closed sets under better replies will be played with positive probability in the limit, as the probability of mistakes tends to zero. If, in addition, the strategy profiles in one such set have strictly higher payoffs than all other strategy profiles and the sample size is sufficiently large, then the strategies in this set will be played with probability one in the limit. Applied to 2x2 Coordination Games, the Pareto dominant equilibrium is selected for a sufficiently large sample size, but in all symmetric and many asymmetric games, the risk dominant equilibrium is selected for a sufficiently small sample size.

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://swopec.hhs.se/hastef/papers/hastef0475.pdf
Download Restriction: no

Paper provided by Stockholm School of Economics in its series SSE/EFI Working Paper Series in Economics and Finance with number 475.

as
in new window

Length: 25 pages
Date of creation: 15 Nov 2001
Date of revision:
Handle: RePEc:hhs:hastef:0475
Contact details of provider: Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
Phone: +46-(0)8-736 90 00
Fax: +46-(0)8-31 01 57
Web page: http://www.hhs.se/
Email:


More information through EDIRC

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.:

as in new window
  1. Weibull, Jörgen W. & Saez-Marti, Maria, 1998. "Clever Agents in Young's Evolutionary Bargaining Model," Working Paper Series 507, Research Institute of Industrial Economics.
  2. Matros, Alexander, 2003. "Clever agents in adaptive learning," Journal of Economic Theory, Elsevier, vol. 111(1), pages 110-124, July.
  3. Ritzberger, Klaus & Weibull, Jörgen W., 1993. "Evolutionary Selection in Normal Form Games," Working Paper Series 383, Research Institute of Industrial Economics.
  4. Kaarboe, O.M. & Tieman, A.F., 1999. "Equilibrium Selection under Different Learning Modes in Supermodular Games," Norway; Department of Economics, University of Bergen 1299, Department of Economics, University of Bergen.
  5. Josephson, Jens, 2001. "A Numerical Analysis of the Evolutionary Stability of Learning Rules," SSE/EFI Working Paper Series in Economics and Finance 474, Stockholm School of Economics.
  6. Antoci, Angelo & Gay, Antonio & Landi, Massimiliano & Sacco, Pier Luigi, 2008. "Global analysis of an expectations augmented evolutionary dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 32(12), pages 3877-3894, December.
  7. Droste, E. & Hommes, C.H. & Tuinstra, J., 1999. "Endogenous Fluctuations under Evolutionary Pressure in Cournot Competition," CeNDEF Working Papers 99-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  8. Hehenkamp, Burkhard & Kaarbøe, Oddvar M., 2003. "Imitators and Optimizers in a Changing Environment," Working Papers in Economics 03/03, University of Bergen, Department of Economics.
  9. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  10. Conlisk, John, 1980. "Costly optimizers versus cheap imitators," Journal of Economic Behavior & Organization, Elsevier, vol. 1(3), pages 275-293, September.
  11. Kaniovski, Yuri M. & Kryazhimskii, Arkadii V. & Young, H. Peyton, 2000. "Adaptive Dynamics in Games Played by Heterogeneous Populations," Games and Economic Behavior, Elsevier, vol. 31(1), pages 50-96, April.
  12. repec:att:wimass:9530 is not listed on IDEAS
  13. Basu, K. & Weibull, J., 1990. "Strategy Subsets Closed Under Rational Behavior," Papers 62, Princeton, Woodrow Wilson School - Discussion Paper.
  14. Carlos Alós-Ferrer, 2001. "Cournot versus Walras in Dynamic Oligopolies with Memory," Vienna Economics Papers 0110, University of Vienna, Department of Economics.
  15. Jens Josephson, 2008. "Stochastic better-reply dynamics in finite games," Economic Theory, Springer, vol. 35(2), pages 381-389, May.
  16. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
  17. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
  18. Juang, Wei-Torng, 2002. "Rule Evolution and Equilibrium Selection," Games and Economic Behavior, Elsevier, vol. 39(1), pages 71-90, April.
  19. Josephson, Jens & Matros, Alexander, 2004. "Stochastic imitation in finite games," Games and Economic Behavior, Elsevier, vol. 49(2), pages 244-259, November.
  20. Van Huyck, John, 2008. "Emergent Conventions in Evolutionary Games," Handbook of Experimental Economics Results, Elsevier.
  21. J. Thijssen, 2005. "Nearly-complete Decomposability and Stochastic Stability with an Application to Cournot Oligopoly," Trinity Economics Papers tep6, Trinity College Dublin, Department of Economics.
  22. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, June.
  23. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
  24. Dawid, Herbert, 2007. "Evolutionary game dynamics and the analysis of agent-based imitation models: The long run, the medium run and the importance of global analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 2108-2133, June.
Full references (including those not matched with items on IDEAS)

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

When requesting a correction, please mention this item's handle: RePEc:hhs:hastef:0475. 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: (Helena Lundin)

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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.