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Reduced strategies and cognitive hierarchies in the extensive and normal form

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  • Battigalli, Pierpaolo

Abstract

In a recent paper, Lin and Palfrey (2024) developed a theory of cognitive hierarchies (CH) in sequential games and observed that this solution concept is not reduced-normal-form invariant. In this paper I qualify and explain this observation. I show that the CH model is normal-form invariant, and that the differences arising from the application of the CH model to the reduced normal form depend only on how randomization by level-0 types is modeled. Indeed, while the uniform behavior strategy in the extensive form yields the uniform mixed strategy in the normal form, the latter does not correspond to the uniform randomization in the reduced normal form, because different reduced strategies may correspond to sets of equivalent strategies with different cardinalities. I also comment on (i) the invariance of the CH model to some transformations of the sequential game, and (ii) the independence of conditional beliefs about co-players’ level-types.

Suggested Citation

  • Battigalli, Pierpaolo, 2026. "Reduced strategies and cognitive hierarchies in the extensive and normal form," Games and Economic Behavior, Elsevier, vol. 158(C), pages 317-329.
    • Handle: RePEc:eee:gamebe:v:158:y:2026:i:c:p:317-329
    DOI: 10.1016/j.geb.2026.03.006
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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
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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