Convergence of best response dynamics in extensive-form games
We prove that, in all finite generic extensive-form games of perfect information, a continuous-time best response dynamic always converges to a Nash equilibrium component. We show the robustness of convergence by an approximate best response dynamic: whatever the initial state and an allowed approximate best response dynamic, the state is close to the set of Nash equilibria most of the time. In a perfect-information game where each player can only move at one node, we prove that all interior approximate best response dynamics converge to the backward induction equilibrium, which is hence the socially stable strategy in the game.
|Date of creation:||24 Jun 2013|
|Date of revision:||28 Jun 2013|
|Note:||The author would like to acknowledge financial support from the Knut and Alice Wallenberg Foundation.|
|Contact details of provider:|| Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden|
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- Hart, Sergiu & Mas-Colell, Andreu, 2003.
"Regret-based continuous-time dynamics,"
Games and Economic Behavior,
Elsevier, vol. 45(2), pages 375-394, November.
- Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, vol. 93(5), pages 1830-1836, December.
- Sergiu Hart, 1999.
"Evolutionary Dynamics and Backward Induction,"
Game Theory and Information
9905002, EconWPA, revised 23 Mar 2000.
- R. Cressman, K.H. Schlag, 1995.
"The Dynamic (In)Stability of Backwards Induction,"
Discussion Paper Serie B
347, University of Bonn, Germany.
- Young, H. Peyton, 2009. "Learning by trial and error," Games and Economic Behavior, Elsevier, vol. 65(2), pages 626-643, March.
- Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, March.
- K. Ritzberger & J. Weibull, 2010.
"Evolutionary Selection in Normal-Form Games,"
Levine's Working Paper Archive
452, David K. Levine.
- M. Kandori & R. Rob, 2010.
"Evolution of Equilibria in the Long Run: A General Theory and Applications,"
Levine's Working Paper Archive
502, David K. Levine.
- Kandori Michihiro & Rob Rafael, 1995. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory, Elsevier, vol. 65(2), pages 383-414, April.
- Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868, December.
- Hart, Sergiu, 1992. "Games in extensive and strategic forms," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 2, pages 19-40 Elsevier.
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