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Learning in games with unstable equilibria

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  • Benaïm, Michel
  • Hofbauer, Josef
  • Hopkins, Ed

Abstract

We propose a new concept for the analysis of games, the TASP, which gives a precise prediction about non-equilibrium play in games whose Nash equilibria are mixed and are unstable under fictitious play-like learning. We show that, when players learn using weighted stochastic fictitious play and so place greater weight on recent experience, the time average of play often converges in these "unstable" games, even while mixed strategies and beliefs continue to cycle. This time average, the TASP, is related to the cycle identified by Shapley [L.S. Shapley, Some topics in two person games, in: M. Dresher, et al. (Eds.), Advances in Game Theory, Princeton University Press, Princeton, 1964]. The TASP can be close to or quite distinct from Nash equilibrium.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 4 (July)
Pages: 1694-1709

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:4:p:1694-1709

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Games Learning Best response dynamics Stochastic fictitious play Mixed strategy equilibria TASP;

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References

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Citations

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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. Martin Hahn, 2012. "An Evolutionary Analysis of Varian’s Model of Sales," Dynamic Games and Applications, Springer, vol. 2(1), pages 71-96, March.
  5. Cason, Timothy N. & Friedman, Daniel & Hopkins, Ed H, 2009. "Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria," Santa Cruz Department of Economics, Working Paper Series qt8kp6c049, Department of Economics, UC Santa Cruz.
  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. Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics.
  9. 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.
  10. Ratul, Lahkar, 2011. "The dynamic instability of dispersed price equilibria," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1796-1827, September.
  11. 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.
  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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