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Minimal belief revision leads to backward induction

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  • Perea, Andrés

Abstract

We present an epistemic model for games with perfect information in which players, upon observing an unexpected move, may revise their belief about the opponents' preferences over outcomes. For a given profile P of preference relations over outcomes, we impose the following conditions: (1) players initially believe that opponents have preference relations as specified by P; (2) players believe at every instance of the game that each opponent is carrying out a sequentially rational strategy; (3) if a player revises his belief about an opponent's type, he must search for a "new" type that disagrees with the "old" type on a minimal number of statements about this opponent; (4) if a player revises his belief about an opponent's preference relation over outcomes, he must search for a "new" preference relation that disagrees with the "old" preference relation on a minimal number of pairwise rankings. It is shown that every player whose preference relation is given by P, and who throughout the game respects common belief in the events (1)-(4), has a unique sequentially rational strategy, namely his backward induction strategy in the game induced by P.

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  • Perea, Andrés, 2008. "Minimal belief revision leads to backward induction," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 1-26, July.
    • Handle: RePEc:eee:matsoc:v:56:y:2008:i:1:p:1-26
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    1. Asheim, Geir B. & Brunnschweiler, Thomas, 2023. "Epistemic foundation of the backward induction paradox," Games and Economic Behavior, Elsevier, vol. 141(C), pages 503-514.
    2. Bach, Christian W. & Heilmann, Conrad, 2009. "Agent connectedness and backward induction," LSE Research Online Documents on Economics 27000, London School of Economics and Political Science, LSE Library.
    3. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Arieli, Itai & Aumann, Robert J., 2015. "The logic of backward induction," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 443-464.
    5. Perea ý Monsuwé, A., 2006. "Epistemic foundations for backward induction: an overview," Research Memorandum 036, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. Graciela Kuechle, 2009. "What Happened To The Three‐Legged Centipede Game?," Journal of Economic Surveys, Wiley Blackwell, vol. 23(3), pages 562-585, July.

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