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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 evolutionary basis for predicting the backwards induction solution in generic finite extensive-form games with perfect information is examined. Evolution is modelled using the replicator dynamic in combination with rare mutations that introduce a small change in the proportion of each strategy. The criterion for our judgement is whether this dynamic stabilizes over time at the subgame perfect equilibrium outcome. We find that the backwards induction solution is fully justified by this process only in simple games; simple meaning two players, two actions at each node and at most three consecutive decisions in the game. Examples of more complex games are given in which this process does not select between the subgame perfect equilibrium outcome and alternative Nash equilibrium outcomes.

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Paper provided by ESRC Centre on Economics Learning and Social Evolution in its series ELSE working papers with number 027.

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Handle: RePEc:els:esrcls:027

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Related research
Keywords: perfect information extensive-form game Centipede Game back- wards induction replicator dynamic 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

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  1. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November. [Downloadable!] (restricted)
  2. 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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  3. 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)
  4. 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)
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(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. 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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  2. 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!]
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  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. 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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  5. Giovanni Ponti, . "Cycles Of Learning In The Centipede Game," ELSE working papers 024, ESRC Centre on Economics Learning and Social Evolution. [Downloadable!]
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  6. Agostino Manduchi, 1998. "Similar Actions and Cooperation in the Centipede Played by Automata," Working Papers 98-06-053, Santa Fe Institute.
  7. Steffen Huck & Joerg Oechssler, 1995. "The Indirect Evolutionary Approach to Explaining Fair Allocations," Game Theory and Information 9507001, EconWPA, revised 27 Aug 1998. [Downloadable!]
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  8. Sergiu Hart, 1999. "Evolutionary Dynamics and Backward Induction," Game Theory and Information 9905002, EconWPA, revised 23 Mar 2000. [Downloadable!]
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