Adaptive learning and p-best response sets
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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Volume (Year): 40 (2011)
Issue (Month): 4 (November)
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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.:
- Akihiko Matsui & Kiminori Matsuyama, 1990.
"An Approach to Equilibrium Selection,"
970, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
- Atsushi Kajii & Stephen Morris, .
""The Robustness of Equilibria to Incomplete Information*'',"
CARESS Working Papres
95-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
- Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
- Atsushi Kajii & Stephen Morris, . "The Robustness of Equilibria to Incomplete Information," Penn CARESS Working Papers ed504c985fc375cbe719b3f60, Penn Economics Department.
- Morris, Stephen & Ui, Takashi, 2005.
"Generalized potentials and robust sets of equilibria,"
Journal of Economic Theory,
Elsevier, vol. 124(1), pages 45-78, September.
- 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.
- Stephen Morris & Takashi Ui, 2003. "Generalized Potentials and Robust Sets of Equilibria," Levine's Working Paper Archive 506439000000000325, David K. Levine.
- smorris & Takashi Ui, 2004. "Generalized Potentials and Robust Sets of Equilibria," Econometric Society 2004 North American Winter Meetings 45, Econometric Society.
- Olivier Tercieux, 2006.
"p-Best response set,"
- Basu, K. & Weibull, J.W., 1990.
"Strategy Subsets Closed Under Rational Behaviour,"
479, Stockholm - International Economic Studies.
- Josef Hofbauer & Daisuke Oyama & Satoru Takahashi, 2004.
"Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics,"
Econometric Society 2004 North American Winter Meetings
339, Econometric Society.
- Oyama, Daisuke & Takahashi, Satoru & Hofbauer, Josef, 2008. "Monotone methods for equilibrium selection under perfect foresight dynamics," Theoretical Economics, Econometric Society, vol. 3(2), June.
- Daisuke Oyama & Satoru Takahashi & Josef Hofbauer, 2003. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," Levine's Bibliography 666156000000000420, UCLA Department of Economics.
- Oyama, Daisuke & Takahashi, Satoru & Hofbauer, Josef, 2003. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," MPRA Paper 6721, University Library of Munich, Germany.
- 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.
- Toshimasa Maruta, 1995.
"On the Relationship Between Risk-Dominance and Stochastic Stability,"
1122, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Maruta, Toshimasa, 1997. "On the Relationship between Risk-Dominance and Stochastic Stability," Games and Economic Behavior, Elsevier, vol. 19(2), pages 221-234, May.
- 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.
- Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
- 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.
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