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More reasoning, fewer outcomes: a monotonicity result for reasoning in dynamic games

Author

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  • Perea, Andrés

    (Maastricht University, Department of Quantitative Economics)

Abstract

A focus function in a dynamic game describes, for every player and each of his information sets, the collection of opponents' information sets he reasons about. Every focus function induces a rationalizability procedure in which a player believes, whenever possible, that his opponents choose rationally at those information sets he reasons about. Under certain conditions, we show that if the players start reasoning about more information sets, then the set of outcomes induced by the associated rationalizability procedure becomes smaller or stays the same. This result does not hold on the level of strategies, unless the players only reason about present and future information sets. The monotonicity result enables us to derive existing theorems, such as the relation in terms of outcomes between forward and backward induction reasoning, but also paves the way for new results.

Suggested Citation

  • Perea, Andrés, 0. "More reasoning, fewer outcomes: a monotonicity result for reasoning in dynamic games," Theoretical Economics, Econometric Society.
    • Handle: RePEc:the:publsh:6814
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    References listed on IDEAS

    as
    1. Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
    2. Perea, Andrés, 2014. "Belief in the opponentsʼ future rationality," Games and Economic Behavior, Elsevier, vol. 83(C), pages 231-254.
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    9. Perea, Andrés, 2018. "Why forward induction leads to the backward induction outcome: A new proof for Battigalli's theorem," Games and Economic Behavior, Elsevier, vol. 110(C), pages 120-138.
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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