Learning Nash Equilibria
In the paper, we re-investigate the long run behavior of an adaptive learning process driven by the stochastic replicator dynamics developed by Fudenberg and Harris (1992). It is demonstrated that the Nash equilibrium will be the robust limit of the adaptive learning process as long as it is reachable for the learning dynamics in almost surely finite time. Doob’s martingale theory and Girsanov Theorem play very important roles in confirming the required assertion.
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- Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
- Tilman B�rgers & Rajiv Sarin, .
"Learning Through Reinforcement and Replicator Dynamics,"
ELSE working papers
051, ESRC Centre on Economics Learning and Social Evolution.
- Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
- T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
- Fudenberg, Drew & Harris, Christopher, 1992.
"Evolutionary Dynamics with Aggregate Shocks,"
IDEI Working Papers
13, Institut d'Économie Industrielle (IDEI), Toulouse.
- Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
- Canning, D., 1990.
"Average Behaviour In Learning Models,"
156, Cambridge - Risk, Information & Quantity Signals.
- Binmore Kenneth G. & Samuelson Larry & Vaughan Richard, 1995. "Musical Chairs: Modeling Noisy Evolution," Games and Economic Behavior, Elsevier, vol. 11(1), pages 1-35, October.
- Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
- Josef Hofbauer & Ed Hopkins, 2004.
"Learning in Perturbed Asymmetric Games,"
ESE Discussion Papers
53, Edinburgh School of Economics, University of Edinburgh.
- 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.
- A. Gaunersdorfer & J. Hofbauer, 2010. "Fictitious Play, Shapley Polygons and the Replicator Equation," Levine's Working Paper Archive 438, David K. Levine.
- A. Cabrales, 2010.
"Stochastic Replicator Dynamics,"
Levine's Working Paper Archive
489, David K. Levine.
- Ellison, Glenn & Fudenberg, Drew, 2000.
"Learning Purified Mixed Equilibria,"
Journal of Economic Theory,
Elsevier, vol. 90(1), pages 84-115, January.
- Glenn Ellison & Drew Fudenberg, 1998. "Learning Purified Mixed Equilibria," Harvard Institute of Economic Research Working Papers 1817, Harvard - Institute of Economic Research.
- Alan Beggs, 2002.
"Stochastic evolution with slow learning,"
Springer, vol. 19(2), pages 379-405.
- Kaniovski Yuri M. & Young H. Peyton, 1995. "Learning Dynamics in Games with Stochastic Perturbations," Games and Economic Behavior, Elsevier, vol. 11(2), pages 330-363, November.
- Binmore, Ken & Samuelson, Larry, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Wiley Blackwell, vol. 66(2), pages 363-93, April.
- 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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