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Rationalizability, observability and common knowledge

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Abstract

We study the strategic impact of players' higher order uncertainty over the observability of actions in general two-player games. More specifically, we consider the space of all belief hierarchies generated by the uncertainty over whether the game will be played as a static game or with perfect information. Over this space, we characterize the correspondence of a solution concept which represents the behavioral implications of Rationality and Common Belief in Rationality (RCBR), where `rationality' is understood as sequential whenever a player moves second. We show that such a correspondence is generically single-valued, and that its structure supports a robust refinement of rationalizability, which often has very sharp implications. For instance: (i) in a class of games which includes both zero-sum games with a pure equilibrium and coordination games with a unique efficient equilibrium, RCBR generically ensures efficient equilibrium outcomes; (ii) in a class of games which also includes other well-known families of coordination games, RCBR generically selects components of the Stackelberg pro les; (iii) if common knowledge is maintained that player 2's action is not observable (e.g., because 1 is commonly known to move earlier, etc.), in a class of games which includes of all the above RCBR generically selects the equilibrium of the static game most favorable to player 1.
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  • Antonio Penta & Peio Zuazo-Garin, 2019. "Rationalizability, observability and common knowledge," Economics Working Papers 1662, Department of Economics and Business, Universitat Pompeu Fabra.
  • Handle: RePEc:upf:upfgen:1662
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    Cited by:

    1. Battigalli, Pierpaolo & Leonetti, Paolo & Maccheroni, Fabio, 2020. "Behavioral equivalence of extensive game structures," Games and Economic Behavior, Elsevier, vol. 121(C), pages 533-547.
    2. Kets, Willemien & Kager, Wouter & Sandroni, Alvaro, 2022. "The value of a coordination game," Journal of Economic Theory, Elsevier, vol. 201(C).
    3. Evan Piermont & Peio Zuazo-Garin, 2021. "Heterogeneously Perceived Incentives in Dynamic Environments: Rationalization, Robustness and Unique Selections," Papers 2105.06772, arXiv.org.
    4. Jann, Ole & Schottmüller, Christoph, 2021. "Regime change games with an active defender," Games and Economic Behavior, Elsevier, vol. 129(C), pages 96-113.

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    More about this item

    Keywords

    eductive coordination; extensive form uncertainty; first-mover advantage; Krpes hypothesis; higher order beliefs; rationalizability; robustness; Stackelberg selections;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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