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A Dynamic Level-k Model in Sequential Games

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  • Teck-Hua Ho

    (National University of Singapore, Singapore 119077; and University of California, Berkeley, Berkeley, California 94720)

  • Xuanming Su

    (The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

Abstract

Backward induction is a widely accepted principle for predicting behavior in sequential games. In the classic example of the "centipede game," however, players frequently violate this principle. An alternative is a "dynamic level-k" model, where players choose a rule from a rule hierarchy. The rule hierarchy is iteratively defined such that the level-k rule is a best response to the level-(k-1) rule, and the level-[infinity] rule corresponds to backward induction. Players choose rules based on their best guesses of others' rules and use historical plays to improve their guesses. The model captures two systematic violations of backward induction in centipede games, limited induction and repetition unraveling. Because the dynamic level-k model always converges to backward induction over repetition, the former can be considered to be a tracing procedure for the latter. We also examine the generalizability of the dynamic level-k model by applying it to explain systematic violations of backward induction in sequential bargaining games. We show that the same model is capable of capturing these violations in two separate bargaining experiments. This paper was accepted by Peter Wakker, decision analysis.

Suggested Citation

  • Teck-Hua Ho & Xuanming Su, 2013. "A Dynamic Level-k Model in Sequential Games," Management Science, INFORMS, vol. 59(2), pages 452-469, March.
  • Handle: RePEc:inm:ormnsc:v:59:y:2013:i:2:p:452-469
    DOI: 10.1287/mnsc.1120.1645
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    2. Penczynski, Stefan P., 2017. "The nature of social learning: Experimental evidence," European Economic Review, Elsevier, vol. 94(C), pages 148-165.
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    5. James Tremewan & Chloé Le Coq & Alexander D. Wagner, 2013. "Social Centipedes: the Impact of Group Identity on Preferences and Reasoning," Vienna Economics Papers 1305, University of Vienna, Department of Economics.
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    11. Wanqun Zhao, 2020. "Cost of Reasoning and Strategic Sophistication," Games, MDPI, Open Access Journal, vol. 11(3), pages 1-27, September.
    12. Matthew Embrey & Guillaume R Fréchette & Sevgi Yuksel, 2018. "Cooperation in the Finitely Repeated Prisoner’s Dilemma," The Quarterly Journal of Economics, Oxford University Press, vol. 133(1), pages 509-551.
    13. Kota Murayama, 2015. "Robust Predictions under Finite Depth of Reasoning," Discussion Paper Series DP2015-28, Research Institute for Economics & Business Administration, Kobe University.
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    18. Benjamin Patrick Evans & Mikhail Prokopenko, 2021. "Bounded rationality for relaxing best response and mutual consistency: An information-theoretic model of partial self-reference," Papers 2106.15844, arXiv.org.
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    20. Tony Haitao Cui & Yinghao Zhang, 2018. "Cognitive Hierarchy in Capacity Allocation Games," Management Science, INFORMS, vol. 64(3), pages 1250-1270, March.
    21. Sheen S. Levine & Mark Bernard & Rosemarie Nagel, 2018. "Strategic intelligence: The cognitive capability to anticipate competitor behaviour," Strategic Management Journal, Wiley Blackwell, vol. 39(2), pages 527-527, February.
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    23. Rineke Verbrugge & Ben Meijering & Stefan Wierda & Hedderik van Rijn & Niels Taatgen, 2018. "Stepwise training supports strategic second-order theory of mind in turn-taking games," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 13(1), pages 79-98, January.
    24. Chen, Chun-Ting & Huang, Chen-Ying & Wang, Joseph Tao-yi, 2018. "A window of cognition: Eyetracking the reasoning process in spatial beauty contest games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 143-158.

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