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The Dynamic (In)Stability of Backwards Induction

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Author Info
R. Cressman, K.H. Schlag

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Abstract

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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File URL: ftp://web.bgse.uni-bonn.de/pub/RePEc/bon/bonsfb/bonsfb347.ps
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Publisher Info
Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 347.

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Date of creation: Dec 1995
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Handle: RePEc:bon:bonsfb:347

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 9221
Web page: http://www.bgse.uni-bonn.de/index.php?id=517

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Related research
Keywords: perfect information; extensive-form game; Centipede Game; backwards induction; replicator dynamics; interior asymptotic stability.;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

References listed on IDEAS
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.:

  1. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, January.
  2. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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  4. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August. [Downloadable!] (restricted)
  5. Hendon, Ebbe & Jacobsen, Hans Jorgen & Sloth, Birgitte, 1996. "Fictitious Play in Extensive Form Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 177-202, August. [Downloadable!] (restricted)
    Other versions:
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Cited by:
(explanations, 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.)

  1. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April. [Downloadable!] (restricted)
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  2. Steffen Huck & Joerg Oechssler, 1995. "The Indirect Evolutionary Approach to Explaining Fair Allocations," Game Theory and Information 9507001, EconWPA, revised 27 Aug 1998. [Downloadable!]
    Other versions:
  3. Demichelis, Stefano & Ritzberger, Klaus & Swinkels, Jeroen M., 2002. "The Simple Geometry of Perfect Information Games," Economics Series 115, Institute for Advanced Studies. [Downloadable!]
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  4. Giovanni B. Ponti, . "Cycles of Learning in the Centipede Game," University of California at Santa Barbara, Economics Working Paper Series 16-97, Department of Economics, UC Santa Barbara. [Downloadable!]
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  5. Francesco Squintani, 2004. "Backward Induction and Model Deterioration," Advances in Theoretical Economics, Berkeley Electronic Press, vol. 4(1), pages 1157-1157. [Downloadable!] (restricted)
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  6. DEMICHELIS, Stefano & RITZBERGER, Klaus, 2000. "From evolutionary to strategic stability," CORE Discussion Papers 2000059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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  7. Steffen Huck & Georg Kirchsteiger & Joerg Oechssler, 1997. "Learning to Like What You Have - Explaining the Endowment Effect," Game Theory and Information 9702001, EconWPA, revised 15 May 1997. [Downloadable!]
    Other versions:
  8. Sergiu Hart, 1999. "Evolutionary Dynamics and Backward Induction," Game Theory and Information 9905002, EconWPA, revised 23 Mar 2000. [Downloadable!]
    Other versions:
  9. Agostino Manduchi, 1998. "Similar Actions and Cooperation in the Centipede Played by Automata," Working Papers 98-06-053, Santa Fe Institute.
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