Advanced Search
MyIDEAS: Login to save this paper or follow this series

Learning in Games with Unstable Equilibria

Contents:

Author Info

  • Ed Hopkins

    ()

  • Josef Hofbauer
  • Michel Benaim

Abstract

We investigate games whose Nash equilibria are mixed and are unstable under fictitious play-like learning processes. We show that when players learn using weighted stochastic fictitious play and so place greater weight on more recent experience that the time average of play often converges in these “unstable” games, even while mixed strategies and beliefs continue to cycle. This time average is related to the best response cycle first identified by Shapley (1964). For many games, the time average is close enough to Nash equilibrium to create the appearance of convergence to equilibrium. We discuss how these theoretical results may help to explain data from recent experimental studies of price dispersion.

Download Info

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://homepages.ed.ac.uk/ehk/unstable.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 135.

as in new window
Length: 36
Date of creation: Jul 2005
Date of revision:
Handle: RePEc:edn:esedps:135

Contact details of provider:
Postal: 31 Buccleuch Place, EH8 9JT, Edinburgh
Phone: +44(0)1316508361
Fax: +44(0)1316504514
Web page: http://www.econ.ed.ac.uk/
More information through EDIRC

Related research

Keywords: Games; Learning; Best Response Dynamics; Stochastic Fictitious Play; Mixed Strategy Equilibria; TASP.;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions; Part II: Applications," Working Papers hal-00242974, HAL.
  2. I. Gilboa & A. Matsui, 2010. "Social Stability and Equilibrium," Levine's Working Paper Archive 534, David K. Levine.
  3. Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Ed Hopkins, . "Learning, Matching and Aggregation," ELSE working papers 033, ESRC Centre on Economics Learning and Social Evolution.
  5. Foster, Dean P. & Young, H. Peyton, 2003. "Learning, hypothesis testing, and Nash equilibrium," Games and Economic Behavior, Elsevier, Elsevier, vol. 45(1), pages 73-96, October.
  6. Jim Engle-Warnick & Ed Hopkins, 2006. "A Simple Test of Learning Theory?," ESE Discussion Papers, Edinburgh School of Economics, University of Edinburgh 153, Edinburgh School of Economics, University of Edinburgh.
  7. Ed Hopkins & Robert M. Seymour, 2002. "The Stability of Price Dispersion under Seller and Consumer Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1157-1190, November.
  8. Benaim, Michel & Weibull, Jörgen W., 2000. "Deterministic Approximation of Stochastic Evolution in Games," Working Paper Series, Research Institute of Industrial Economics 534, Research Institute of Industrial Economics, revised 30 Oct 2001.
  9. Brown-Kruse, Jamie, et al, 1994. "Bertrand-Edgeworth Competition in Experimental Markets," Econometrica, Econometric Society, Econometric Society, vol. 62(2), pages 343-72, March.
  10. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780199269181, October.
  11. Viossat, Yannick, 2007. "The replicator dynamics does not lead to correlated equilibria," Games and Economic Behavior, Elsevier, Elsevier, vol. 59(2), pages 397-407, May.
  12. Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information, EconWPA 9703006, EconWPA, revised 24 Mar 1997.
  13. R. McKelvey & T. Palfrey, 2010. "Quantal Response Equilibria for Normal Form Games," Levine's Working Paper Archive 510, David K. Levine.
  14. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, Elsevier, vol. 11(2), pages 279-303, November.
  15. Cason, Timothy N. & Friedman, Daniel, 2003. "Buyer search and price dispersion: a laboratory study," Journal of Economic Theory, Elsevier, Elsevier, vol. 112(2), pages 232-260, October.
  16. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 1999. "The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies," Virginia Economics Online Papers 332, University of Virginia, Department of Economics.
  17. Ellison, Glenn & Fudenberg, Drew, 2000. "Learning Purified Mixed Equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 90(1), pages 84-115, January.
  18. Ed Hopkins, 2004. "Two Competing Models of How People Learn in Games," ESE Discussion Papers, Edinburgh School of Economics, University of Edinburgh 51, Edinburgh School of Economics, University of Edinburgh.
  19. Ed Hopkins, . "A Note on Best Response Dynamics," ESE Discussion Papers, Edinburgh School of Economics, University of Edinburgh 3, Edinburgh School of Economics, University of Edinburgh.
  20. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  21. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2003. "Stochastic Approximations and Differential Inclusions," Working Papers hal-00242990, HAL.
  22. Battalio, Raymond & Samuelson, Larry & Van Huyck, John, 2001. "Optimization Incentives and Coordination Failure in Laboratory Stag Hunt Games," Econometrica, Econometric Society, Econometric Society, vol. 69(3), pages 749-64, May.
  23. Anderson, Christopher M. & Granat, Sander & Plott, Charles R. & Shimomura, Ken-Ichi, 2000. "Global Instability in Experimental General Equilibrium: The Scarf Example," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 1086, California Institute of Technology, Division of the Humanities and Social Sciences.
  24. Tang, Fang-Fang, 2001. "Anticipatory learning in two-person games: some experimental results," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 44(2), pages 221-232, February.
  25. Viossat, Yannick, 2004. "Replicator Dynamics and Correlated Equilibrium," Economics Papers from University Paris Dauphine 123456789/5219, Paris Dauphine University.
  26. Morgan, John & Orzen, Henrik & Sefton, Martin, 2006. "An experimental study of price dispersion," Games and Economic Behavior, Elsevier, Elsevier, vol. 54(1), pages 134-158, January.
  27. Cason, Timothy N. & Friedman, Daniel & Wagener, Florian, 2005. "The dynamics of price dispersion, or Edgeworth variations," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 29(4), pages 801-822, April.
  28. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
  29. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, Elsevier, vol. 42(3-5), pages 631-639, May.
  30. C. Monica Capra & Jacob K. Goeree & Rosario Gomez & Charles A. Holt, 2000. "Learning and Noisy Equilibrium Behavior in an Experimental Study of Imperfect Price Competition," Virginia Economics Online Papers 336, University of Virginia, Department of Economics.
  31. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, Econometric Society, vol. 51(4), pages 955-69, July.
  32. Cheung, Yin-Wong & Friedman, Daniel, 1997. "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, Elsevier, Elsevier, vol. 19(1), pages 46-76, April.
  33. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, American Economic Association, vol. 70(4), pages 651-59, September.
  34. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 10(1), pages 6-38, July.
  35. Brown, James N & Rosenthal, Robert W, 1990. "Testing the Minimax Hypothesis: A Re-examination of O'Neill's Game Experiment," Econometrica, Econometric Society, Econometric Society, vol. 58(5), pages 1065-81, September.
  36. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, Elsevier, vol. 52(1), pages 133-152, July.
  37. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, Elsevier, vol. 68(1), pages 258-265, January.
  38. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 29(1-2), pages 36-72, October.
  39. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, Econometric Society, vol. 67(4), pages 827-874, July.
  40. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, Econometric Society, vol. 70(6), pages 2265-2294, November.
  41. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, American Economic Association, vol. 88(4), pages 848-81, September.
  42. Yannick Viossat, 2005. "Replicator Dynamics and Correlated Equilibrium: Elimination of All Strategies in the Support of Correlated Equilibria," Working Papers hal-00242977, HAL.
Full references (including those not matched with items on IDEAS)

Citations

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

Cited by:
  1. Friedman, Daniel & Cason, Timothy N & Hopkins, Ed, 2012. "Cycles and Instability in a Rock-Paper-Scissors Population Game: a Continuous Time Experiment," Santa Cruz Department of Economics, Working Paper Series qt6947v2f5, Department of Economics, UC Santa Cruz.
  2. Jim Engle-Warnick & Ed Hopkins, 2006. "A Simple Test of Learning Theory," CIRANO Working Papers, CIRANO 2006s-30, CIRANO.
  3. García-Gallego, Aurora & Georgantzís, Nikolaos & Jaramillo-Gutiérrez, Ainhoa & Pereira, Pedro & Pernías-Cerrillo, J. Carlos, 2014. "On the evolution of monopoly pricing in Internet-assisted search markets," Journal of Business Research, Elsevier, Elsevier, vol. 67(5), pages 795-801.
  4. Timothy N. Cason & Daniel Friedman & Ed Hopkins, 2009. "Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria," ESE Discussion Papers, Edinburgh School of Economics, University of Edinburgh 188, Edinburgh School of Economics, University of Edinburgh.
  5. Drew Fudenberg & Satoru Takahashi, 2008. "Heterogeneous Beliefs and Local Information in Stochastic Fictitious Play," Levine's Working Paper Archive 122247000000001695, David K. Levine.
  6. Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics.
  7. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 146(5), pages 1796-1827, September.
  8. Roger Waldeck & Eric Darmon, 2006. "Can boundedly rational sellers learn to play Nash?," Journal of Economic Interaction and Coordination, Springer, vol. 1(2), pages 147-169, November.
  9. Martin Hahn, 2012. "An Evolutionary Analysis of Varian’s Model of Sales," Dynamic Games and Applications, Springer, Springer, vol. 2(1), pages 71-96, March.
  10. Georgios Chasparis & Jeff Shamma, 2012. "Distributed Dynamic Reinforcement of Efficient Outcomes in Multiagent Coordination and Network Formation," Dynamic Games and Applications, Springer, Springer, vol. 2(1), pages 18-50, March.
  11. Ulrich Berger, 2012. "Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play," Dynamic Games and Applications, Springer, Springer, vol. 2(1), pages 4-17, March.
  12. Hommes, Cars H. & Ochea, Marius I., 2012. "Multiple equilibria and limit cycles in evolutionary games with Logit Dynamics," Games and Economic Behavior, Elsevier, Elsevier, vol. 74(1), pages 434-441.

Lists

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

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:edn:esedps:135. 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: (Gina Reddie).

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.