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Backward induction reasoning beyond backward induction

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  • Emiliano Cantonini
  • Antonio Penta

Abstract

Backward Induction is only defined for games with perfect information, but its logic is also invoked in many equilibrium concepts for games with imperfect or incomplete information. Yet, the meaning of 'backward induction reasoning' is unclear in these settings, and we lack a way to apply its simple logic to general games. We remedy this by introducing a solution concept, Backwards Rationalizability, that satisfies several properties normally ascribed to backward induction reasoning, foremost the possibility of being computed via a tractable backwards procedure. We also show that Backwards Rationalizability characterizes the robust predictions of a 'perfect equilibrium' notion that introduces the backward induction logic and nothing more into equilibrium analysis. We discuss a few applications, including a new version of peer-confirming equilibrium (Lipnowski and Sadler (2019)) that, thanks to Backwards Rationalizability, restores in dynamic games the natural comparative statics that the original concept only displays in static settings.

Suggested Citation

  • Emiliano Cantonini & Antonio Penta, 2024. "Backward induction reasoning beyond backward induction," Economics Working Papers 1894, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1894
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    References listed on IDEAS

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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    2. Mariann Ollar & Antonio Penta, 2023. "A network solution to robust implementation: the case of identical but unknown distributions," Post-Print hal-04198678, HAL.
    3. Mariann Ollár & Antonio Penta, 2023. "A Network Solution to Robust Implementation: The Case of Identical but Unknown Distributions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(5), pages 2517-2554.
    4. Dirk Bergemann & Stephen Morris, 2012. "An Ascending Auction for Interdependent Values: Uniqueness and Robustness to Strategic Uncertainty," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 7, pages 253-262, World Scientific Publishing Co. Pte. Ltd..
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    Keywords

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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