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Cognitive Hierarchy Theory and Two-Person Games

Author

Listed:
  • Carlos Gracia-Lázaro

    (Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018 Zaragoza, Spain)

  • Luis Mario Floría

    (Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018 Zaragoza, Spain
    Departamento de Física de la Materia Condensada, University of Zaragoza, 50009 Zaragoza, Spain)

  • Yamir Moreno

    (Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, 50018 Zaragoza, Spain
    Departamento de Física Teórica, University of Zaragoza, 50009 Zaragoza, Spain)

Abstract

The outcome of many social and economic interactions, such as stock-market transactions, is strongly determined by the predictions that agents make about the behavior of other individuals. Cognitive hierarchy theory provides a framework to model the consequences of forecasting accuracy that has proven to fit data from certain types of game theory experiments, such as Keynesian beauty contests and entry games. Here, we focus on symmetric two-player-two-action games and establish an algorithm to find the players’ strategies according to the cognitive hierarchy approach. We show that the snowdrift game exhibits a pattern of behavior whose complexity grows as the cognitive levels of players increases. In addition to finding the solutions up to the third cognitive level, we demonstrate, in this theoretical frame, two new properties of snowdrift games: (i) any snowdrift game can be characterized by only a parameter, its class; (ii) they are anti-symmetric with respect to the diagonal of the pay-off’s space. Finally, we propose a model based on an evolutionary dynamics that captures the main features of the cognitive hierarchy theory.

Suggested Citation

  • Carlos Gracia-Lázaro & Luis Mario Floría & Yamir Moreno, 2017. "Cognitive Hierarchy Theory and Two-Person Games," Games, MDPI, vol. 8(1), pages 1-18, January.
    • Handle: RePEc:gam:jgames:v:8:y:2017:i:1:p:1-:d:86780
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    References listed on IDEAS

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    1. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
    2. Tanjim Hossain & John Morgan, 2013. "When Do Markets Tip? A Cognitive Hierarchy Approach," Marketing Science, INFORMS, vol. 32(3), pages 431-453, May.
    3. Vincent P. Crawford & Nagore Iriberri, 2007. "Level-k Auctions: Can a Nonequilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions?," Econometrica, Econometric Society, vol. 75(6), pages 1721-1770, November.
    4. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
    5. Eyal Winter & Amnon Rapoport & Darryl A. Seale, 2000. "An experimental study of coordination and learning in iterated two-market entry games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(3), pages 661-687.
    6. Bramoulle, Yann, 2007. "Anti-coordination and social interactions," Games and Economic Behavior, Elsevier, vol. 58(1), pages 30-49, January.
    7. Vincent P. Crawford & Nagore Iriberri, 2007. "Fatal Attraction: Salience, Naivete, and Sophistication in Experimental Hide-and-Seek Games," Levine's Bibliography 321307000000000861, UCLA Department of Economics.
    8. Erev, Ido & Rapoport, Amnon, 1998. "Coordination, "Magic," and Reinforcement Learning in a Market Entry Game," Games and Economic Behavior, Elsevier, vol. 23(2), pages 146-175, May.
    9. Darrough, Masako N. & Stoughton, Neal M., 1990. "Financial disclosure policy in an entry game," Journal of Accounting and Economics, Elsevier, vol. 12(1-3), pages 219-243, January.
    10. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 861-898.
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    Cited by:

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