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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 321307000000000547.

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Date of creation: 27 Oct 2006
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Handle: RePEc:cla:levrem:321307000000000547

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Citations

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Cited by:
  1. Cason, Timothy N. & Friedman, Daniel & Hopkins, Ed, 2010. "Testing the TASP: An experimental investigation of learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2309-2331, November.
  2. 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.
  3. Aurora García-Gallego & Nikolaos Georgantzis & Ainhoa Jaramillo-Gutiérrez & Pedro Pereira & J. Carlos Pernías-Cerrillo, 2013. "On the evolution of monopoly pricing in Internet-assisted search markets," Working Papers 2013/05, Economics Department, Universitat Jaume I, Castellón (Spain).
  4. 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.
  5. Jim Engle-Warnick & Ed Hopkins, 2006. "A Simple Test of Learning Theory," CIRANO Working Papers 2006s-30, CIRANO.
  6. Drew Fudenberg & Satoru Takahashi, 2008. "Heterogeneous Beliefs and Local Information in Stochastic Fictitious Play," Levine's Working Paper Archive 122247000000001695, David K. Levine.
  7. Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics.
  8. Martin Hahn, 2012. "An Evolutionary Analysis of Varian’s Model of Sales," Dynamic Games and Applications, Springer, vol. 2(1), pages 71-96, March.
  9. Ulrich Berger, 2012. "Non-algebraic Convergence Proofs for Continuous-Time Fictitious Play," Dynamic Games and Applications, Springer, vol. 2(1), pages 4-17, March.
  10. 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.
  11. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
  12. 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.

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