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Level-k analysis of experimental centipede games

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  • Kawagoe, Toshiji
  • Takizawa, Hirokazu

Abstract

As one of the best-known examples of the paradox of backward induction, centipede games have prompted a host of studies with various approaches and explanations (McKelvey and Palfrey, 1992; Fey et al., 1996; Nagel and Tang, 1998; Rapoport et al., 2003; Palacios-Huerta and Volij, 2009). Focusing on initial plays observed in experiments, this paper attempts to offer another explanation based on thorough study of level-k models as applied to these games. Borrowing ideas from the cognitive hierarchy model (Camerer et al., 2004), the authors constructed a group of models based on levels of rationality, and also tested for various assumptions on the play of the most naïve player type in these models. It was found that level-k models generally perform better than the agent quantal response equilibrium (AQRE) model and its variant with altruistic player types for increasing-pie centipede games, while the AQRE model with altruistic player types performs better in constant-pie games.

Suggested Citation

  • Kawagoe, Toshiji & Takizawa, Hirokazu, 2012. "Level-k analysis of experimental centipede games," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 548-566.
  • Handle: RePEc:eee:jeborg:v:82:y:2012:i:2:p:548-566
    DOI: 10.1016/j.jebo.2012.03.010
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    Cited by:

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    2. Eva M. Krockow & Masanori Takezawa & Briony D. Pulford & Andrew M. Colman & Samuel Smithers & Toshimasa Kita & Yo Nakawake, 2018. "Commitment-enhancing tools in Centipede games: Evidencing European–Japanese differences in trust and cooperation," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 13(1), pages 61-72, January.
    3. Aniol Llorente-Saguer & Roman M. Sheremeta & Nora Szech, 2016. "Designing Contests Between Heterogeneous Contestants: An Experimental Study of Tie-Breaks and Bid-Caps in All-Pay Auctions," CESifo Working Paper Series 5955, CESifo.
    4. Yun Wang, 2015. "Belief and Higher-Order Belief in the Centipede Games: Theory and Experiment," Working Papers 2015-03-24, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    5. Quement, Mark T. Le & Marcin, Isabel, 2020. "Communication and voting in heterogeneous committees: An experimental study," Journal of Economic Behavior & Organization, Elsevier, vol. 174(C), pages 449-468.
    6. Volker Benndorf & Dorothea Kübler & Hans-Theo Normann, 2017. "Depth of Reasoning and Information Revelation: An Experiment on the Distribution of k-Levels," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-18, December.
    7. Ganglmair, Bernhard & Holcomb, Alex & Myung, Noah, 2020. "Expectations of reciprocity when competitors share information: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 170(C), pages 244-267.
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    9. Georganas, Sotiris & Healy, Paul J. & Weber, Roberto A., 2015. "On the persistence of strategic sophistication," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 369-400.
    10. Choo, Lawrence C.Y & Kaplan, Todd R., 2014. "Explaining Behavior in the "11-20" Game," MPRA Paper 52808, University Library of Munich, Germany.
    11. 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.
    12. Paolo Crosetto & Marco Mantovani, 2018. "Representation effects in the centipede game," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-13, October.
    13. Gamba, Astrid & Regner, Tobias, 2019. "Preferences-dependent learning in the centipede game: The persistence of mistrust," European Economic Review, Elsevier, vol. 120(C).
    14. Llorente-Saguer, Aniol & Sheremeta, Roman & Szech, Nora, 2020. "Designing Contests Between Heterogeneous Contestants: An Experimental Studie of Tie-Breaks and Bid-Caps in All-Pay Auctions," VfS Annual Conference 2020 (Virtual Conference): Gender Economics 224585, Verein für Socialpolitik / German Economic Association.
    15. Mark T. Le Quement & Isabel Marcin, 2016. "Communication and voting in heterogeneous committees: An experimental study," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2016_05, Max Planck Institute for Research on Collective Goods, revised Oct 2016.
    16. Le Coq, Chloé & Tremewan, James & Wagner, Alexander K., 2015. "On the effects of group identity in strategic environments," European Economic Review, Elsevier, vol. 76(C), pages 239-252.
    17. Bernardo García-Pola & Nagore Iriberri & Jaromír Kovářík, 2020. "Hot versus cold behavior in centipede games," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 6(2), pages 226-238, December.
    18. Bayer, R.-C. & Renou, Ludovic, 2016. "Logical abilities and behavior in strategic-form games," Journal of Economic Psychology, Elsevier, vol. 56(C), pages 39-59.
    19. Li, Xiaolin & Özer, Özalp & Subramanian, Upender, 2021. "Are we strategically naïve or guided by trust and trustworthiness in cheap-talk communication?," LSE Research Online Documents on Economics 107103, London School of Economics and Political Science, LSE Library.
    20. Oren Bar-Gill & Christoph Engel, 2020. "Property is Dummy Proof: An Experiment," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2020_02, Max Planck Institute for Research on Collective Goods.
    21. Eva M. Krockow & Briony D. Pulford & Andrew M. Colman, 2015. "Competitive Centipede Games: Zero-End Payoffs and Payoff Inequality Deter Reciprocal Cooperation," Games, MDPI, Open Access Journal, vol. 6(3), pages 1-11, August.

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    More about this item

    Keywords

    Centipede game; Level-k analysis; Bounded rationality; Altruism; 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
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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