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The Dynamic (In)Stability of Backwards Induction

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  • R. Cressman
  • K.H. Schlag

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.

Suggested Citation

  • R. Cressman & K.H. Schlag, "undated". "The Dynamic (In)Stability of Backwards Induction," ELSE working papers 027, ESRC Centre on Economics Learning and Social Evolution.
    • Handle: RePEc:els:esrcls:027
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    References listed on IDEAS

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    More about this item

    Keywords

    perfect information; extensive-form game; Centipede Game; back- wards induction; replicator dynamic; interior asymptotic stability.;
    All these keywords.

    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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