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The Dynamic (In)Stability of Backwards Induction

Listed author(s):
  • Cressman, R.
  • Schlag, K. H.

The analysis of the replicator dynamic in generic perfect information games yields the following results. In the long run, players play a Nash equilibrium provided that initially all strategies are present. There is at most one ``stable'' component (formally, an interior asymptotically stable set), play in this component will follow the backwards induction path. Existence of such a component is guaranteed in games with at most three consecutive decision nodes. An example of a ``longer'' game is provided where some trajectories starting close to the backwards induction component lead away and never come back.

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

Volume (Year): 83 (1998)
Issue (Month): 2 (December)
Pages: 260-285

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Handle: RePEc:eee:jetheo:v:83:y:1998:i:2:p:260-285
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. van Damme, E.E.C., 1984. "A relation between perfect equilibria in extensive form games and proper equilibria in normal form games," Other publications TiSEM 3734d89e-fd5c-4c80-a230-5, Tilburg University, School of Economics and Management.
  2. Ritzberger, Klaus & Weibull, Jörgen W., 1993. "Evolutionary Selection in Normal Form Games," Working Paper Series 383, Research Institute of Industrial Economics.
  3. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
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