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Adaptive learning and p-best response sets

  • J. Durieu


  • P. Solal


  • O. Tercieux


A product set of strategies is a p-best response set if for each agent it contains all best responses to any distribution placing at least probability p on his opponents' profiles belonging to the product set. A p-best response set is minimal if it does not properly contain another p-best response set. We study a perturbed joint fictitious play process with bounded memory and sample and a perturbed independent fictitious play process as in Young (Econometrica 61:57-84, ). We show that in n-person games only strategies contained in the unique minimal p-best response set can be selected in the long run by both types of processes provided that the rate of perturbations and p are sufficiently low. For each process, an explicit bound of p is given and we analyze how this critical value evolves when n increases. Our results are robust to the degree of incompleteness of sampling relative to memory.

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Article provided by Springer & Game Theory Society in its journal International Journal of Game Theory.

Volume (Year): 40 (2011)
Issue (Month): 4 (November)
Pages: 735-747

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Handle: RePEc:spr:jogath:v:40:y:2011:i:4:p:735-747
DOI: 10.1007/s00182-010-0266-2
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  1. Olivier Tercieux, 2006. "p-Best response set," Post-Print halshs-00754120, HAL.
  2. Basu, K. & Weibull, J.W., 1990. "Strategy Subsets Closed Under Rational Behaviour," Papers 479, Stockholm - International Economic Studies.
  3. 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, December.
  4. Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
  5. Deisuke Oyama & Satoru Takahashi & Josef Hofbauer, 2003. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," Vienna Economics Papers 0318, University of Vienna, Department of Economics.
  6. Toshimasa Maruta, 1995. "On the Relationship Between Risk-Dominance and Stochastic Stability," Discussion Papers 1122, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
  8. Stephen Morris & Takashi Ui, 2003. "Generalized Potentials and Robust Sets of Equilibria," Cowles Foundation Discussion Papers 1394, Cowles Foundation for Research in Economics, Yale University.
  9. Akihiko Matsui & Kiminori Matsuyama, 1990. "An Approach to Equilibrium Selection," Discussion Papers 970, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  11. Kojima, Fuhito & Takahashi, Satoru, 2008. "p-Dominance and perfect foresight dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 67(3-4), pages 689-701, September.
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