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Learning in Games with Unstable Equilibria

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  • Michel Benaim
  • Josef Hofbauer
  • Ed Hopkins

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.

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Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 784828000000000609.

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Date of creation: 21 Nov 2005
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Handle: RePEc:cla:levrem:784828000000000609

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  1. Burdett, Kenneth & Judd, Kenneth L, 1983. "Equilibrium Price Dispersion," Econometrica, Econometric Society, vol. 51(4), pages 955-69, July.
  2. Jim Engle-Warnick & Ed Hopkins, 2006. "A Simple Test of Learning Theory?," ESE Discussion Papers 153, Edinburgh School of Economics, University of Edinburgh.
  3. Morgan, John & Orzen, Henrik & Sefton, Martin, 2006. "An experimental study of price dispersion," Games and Economic Behavior, Elsevier, vol. 54(1), pages 134-158, January.
  4. 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, vol. 43(4), pages 1157-1190, November.
  5. Timothy N. Cason & Daniel Friedman, 2000. "Buyer Search and Price Dispersion: A Laboratory Study," Econometric Society World Congress 2000 Contributed Papers 1549, Econometric Society.
  6. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions; Part II: Applications," Working Papers hal-00242974, HAL.
  7. Glenn Ellison & Drew Fudenberg, 1998. "Learning Purified Mixed Equilibria," Harvard Institute of Economic Research Working Papers 1817, Harvard - Institute of Economic Research.
  8. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  9. Battalio, Raymond & Samuelson, Larry & Van Huyck, John, 2001. "Optimization Incentives and Coordination Failure in Laboratory Stag Hunt Games," Econometrica, Econometric Society, vol. 69(3), pages 749-64, May.
  10. Ed Hopkins, . "Learning, Matching and Aggregation," ESE Discussion Papers 2, Edinburgh School of Economics, University of Edinburgh.
  11. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September.
  12. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, 05.
  13. Viossat, Yannick, 2004. "Replicator Dynamics and Correlated Equilibrium," Economics Papers from University Paris Dauphine 123456789/5219, Paris Dauphine University.
  14. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2002. "The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies," Southern Economic Journal, Southern Economic Association, vol. 69(1), pages 21-47, July.
  15. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181.
  16. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
  17. Tang, Fang-Fang, 2001. "Anticipatory learning in two-person games: some experimental results," Journal of Economic Behavior & Organization, Elsevier, vol. 44(2), pages 221-232, February.
  18. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January.
  19. Ed Hopkins, 2004. "Two Competing Models of How People Learn in Games," ESE Discussion Papers 51, Edinburgh School of Economics, University of Edinburgh.
  20. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May.
  21. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
  22. Sergiu Hart & Andreu Mas-Colell, 1996. "A simple adaptive procedure leading to correlated equilibrium," Economics Working Papers 200, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1996.
  23. Anderson, Christopher M. & Granat, Sander & Plott, Charles R. & Shimomura, Ken-Ichi, 2000. "Global Instability in Experimental General Equilibrium: The Scarf Example," Working Papers 1086, California Institute of Technology, Division of the Humanities and Social Sciences.
  24. Michel Benaim & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions II: Applications," Levine's Bibliography 784828000000000098, UCLA Department of Economics.
  25. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  26. Ed Hopkins, . "A Note on Best Response Dynamics," ESE Discussion Papers 3, Edinburgh School of Economics, University of Edinburgh.
  27. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
  28. Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
  29. R. McKelvey & T. Palfrey, 2010. "Quantal Response Equilibria for Normal Form Games," Levine's Working Paper Archive 510, David K. Levine.
  30. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
  31. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
  32. Viossat, Yannick, 2007. "The Replicator Dynamics Does not Lead to Correlated Equilibria," Economics Papers from University Paris Dauphine 123456789/1061, Paris Dauphine University.
  33. Cason, Timothy N. & Friedman, Daniel & Wagener, Florian, 2005. "The dynamics of price dispersion, or Edgeworth variations," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 801-822, April.
  34. 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, vol. 88(4), pages 848-81, September.
  35. 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.
  36. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  37. Brown, James N & Rosenthal, Robert W, 1990. "Testing the Minimax Hypothesis: A Re-examination of O'Neill's Game Experiment," Econometrica, Econometric Society, vol. 58(5), pages 1065-81, September.
  38. Brown-Kruse, Jamie, et al, 1994. "Bertrand-Edgeworth Competition in Experimental Markets," Econometrica, Econometric Society, vol. 62(2), pages 343-72, March.
  39. Cheung, Yin-Wong & Friedman, Daniel, 1997. "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, Elsevier, vol. 19(1), pages 46-76, April.
  40. Yannick Viossat, 2005. "Replicator Dynamics and Correlated Equilibrium: Elimination of All Strategies in the Support of Correlated Equilibria," Working Papers hal-00242977, HAL.
  41. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2003. "Stochastic Approximations and Differential Inclusions," Working Papers hal-00242990, HAL.
  42. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
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Citations

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Cited by:
  1. 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.
  2. Timothy N. Cason & Daniel Friedman & Ed Hopkins, 2009. "Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria," ESE Discussion Papers 188, Edinburgh School of Economics, University of Edinburgh.
  3. Timothy N. Cason & Daniel Friedman & ED Hopkins, 2014. "Cycles and Instability in a Rock--Paper--Scissors Population Game: A Continuous Time Experiment," Review of Economic Studies, Oxford University Press, vol. 81(1), pages 112-136.
  4. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
  5. Hommes, Cars H. & Ochea, Marius I., 2012. "Multiple equilibria and limit cycles in evolutionary games with Logit Dynamics," Games and Economic Behavior, Elsevier, vol. 74(1), pages 434-441.
  6. Jim Engle-Warnick & Ed Hopkins, 2006. "A Simple Test of Learning Theory," Levine's Bibliography 321307000000000724, UCLA Department of Economics.
  7. Ulrich Berger, 2012. "Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play," Dynamic Games and Applications, Springer, vol. 2(1), pages 4-17, March.
  8. Fudenberg, Drew & Takahashi, Satoru, 2011. "Heterogeneous beliefs and local information in stochastic fictitious play," Games and Economic Behavior, Elsevier, vol. 71(1), pages 100-120, January.
  9. Martin Hahn, 2012. "An Evolutionary Analysis of Varian’s Model of Sales," Dynamic Games and Applications, Springer, vol. 2(1), pages 71-96, March.
  10. Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics.
  11. 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, vol. 67(5), pages 795-801.
  12. Georgios Chasparis & Jeff Shamma, 2012. "Distributed Dynamic Reinforcement of Efficient Outcomes in Multiagent Coordination and Network Formation," Dynamic Games and Applications, Springer, vol. 2(1), pages 18-50, March.

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