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Magic Mirror on the Wall, Who Is the Smartest One of All?

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  • Yoram Halevy
  • Johannes C. Hoelzemann
  • Terri Kneeland

Abstract

In the leading model of bounded rationality in games, each player best-responds to their belief that the other players reason to some finite level. This paper investigates a novel behavior that could reveal if the player’s belief lies outside the iterative reasoning model. This encompasses a situation where a player believes that their opponent can reason to a higher level than they do. We propose an identification strategy for such behavior, and evaluate it experimentally.

Suggested Citation

  • Yoram Halevy & Johannes C. Hoelzemann & Terri Kneeland, 2025. "Magic Mirror on the Wall, Who Is the Smartest One of All?," Working Papers tecipa-789, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-789
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    More about this item

    Keywords

    Bounded rationality; higher-order rationality; level-k; cognitive-hierarchy; game theory; equilibrium; rationalizability; preference elicitation; lab experiment;
    All these keywords.

    JEL classification:

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