Abstract
Level-k thinking has been widely applied as a solution concept for games in normal form in behavioral and experimental game theory. We consider level-k thinking in games in extensive form. Player’s may learn about levels of opponents’ thinking during the play of the game because some information sets may be inconsistent with certain levels. In particular, for any information set reached, a level-k player attaches the maximum level-\(\ell \) thinking for \(\ell < k\) to her opponents consistent with the information set. We compare our notion of strong level-k thinking with other solution concepts such as level-k thinking in the associated normal form, strong rationalizability, \(\Delta \)-rationalizability, iterated admissibility, backward rationalizability, backward level-k thinking, and backward induction. We use strong level-k thinking to reanalyze data from some prior experiments in the literature.
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We thank the editor and two anonymous reviewers for their helpful comments. We thank Dieter Balkenborg, Russell Cooper, Douglas De Jong, Pietr Evdokimov, Rosemarie Nagel, Thomas Ross, and Aldo Rustichini for sharing their data with us. We also thank participants in the Bay Area Experimental Workshop, 2019, for helpful comments. Hang gratefully acknowledges financial support from the Shanghai Rising-Star Program under Grant No. 23AQ1403200. Burkhard gratefully acknowledges financial support via ARO Contract W911NF2210282. A prior version of the paper was titled “Extensive-form level-k”.
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Schipper, B.C., Zhou, H. Level-k thinking in the extensive form. Econ Theory (2024). https://doi.org/10.1007/s00199-024-01556-x
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DOI: https://doi.org/10.1007/s00199-024-01556-x
Keywords
- Level-k thinking
- Cognitive hierarchy
- Theory-of-mind
- Rationalizability
- Iterated admissibility
- Strong rationalizability
- Extensive-form rationalizability
- \(\Delta \)-rationalizability
- Forward induction
- Backward rationalizability
- Backward induction
- k-level mutual belief in rationality
- Experimental game theory