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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:

    1. Garcia-Pola, Bernardo & Iriberri, Nagore & Kovarik, Jaromir, 2016. "Non-equilibrium Play in Centipede Games," CEPR Discussion Papers 11477, C.E.P.R. Discussion Papers.
    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. Llorente-Saguer, Aniol & Sheremeta, Roman M. & Szech, Nora, 2016. "Designing contests between heterogeneous contestants: An experimental study of tie-breaks and bid-caps in all-pay auctions," Working Paper Series in Economics 88, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
    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. 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.
    6. 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 Group Munich.
    7. Benndorf, Volker & Kübler, Dorothea & Normann, Hans-Theo, 2015. "Privacy concerns, voluntary disclosure of information, and unraveling: An experiment," European Economic Review, Elsevier, vol. 75(C), pages 43-59.
    8. 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.
    9. 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.
    10. Sotiris Georganas & Paul J. Healy & Roberto A. Weber, 2014. "On the Persistence of Strategic Sophistication," CESifo Working Paper Series 4653, CESifo Group Munich.
    11. 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.
    12. Choo, Lawrence C.Y & Kaplan, Todd R., 2014. "Explaining Behavior in the "11-20" Game," MPRA Paper 52808, University Library of Munich, Germany.
    13. 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.
    14. Paolo Crosetto & Marco Mantovani, 2018. "Representation effects in the centipede game," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-13, October.
    15. Gamba, Astrid & Regner, Tobias, 2019. "Preferences-dependent learning in the centipede game: The persistence of mistrust," European Economic Review, Elsevier, vol. 120(C).
    16. 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.
    17. 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.

    More about this item

    Keywords

    Centipede game; Level-k analysis; Bounded rationality; Altruism; Experiment;

    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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