IDEAS home Printed from https://ideas.repec.org/p/cda/wpaper/356.html
   My bibliography  Save this paper

Higher-order beliefs in a Sequential Social Dilemma

Author

Listed:
  • Anujit Chakraborty
  • Evan Calford

    (Department of Economics, University of California Davis)

Abstract

Do experimental subjects have consistent first and higher-order beliefs about others? How does any inconsistency affect strategic decisions? We introduce a simple four-player sequential social dilemma where actions reveal first and higher-order beliefs. The unique sub-game perfect Nash equilibrium (SPNE) is observed less than 5% of the time, even though our diagnostic treatments show that a majority of our subjects are self-interested, higher-order rational and have accurate first-order beliefs. In our data, strategic play deviates substantially from Nash predictions because first-order and higher-order beliefs are inconsistent for most subjects. We construct and operationalize an epistemic model of belief hierarchies to estimate that less than 10% of subjects have consistent first and higher-order beliefs.

Suggested Citation

  • Anujit Chakraborty & Evan Calford, 2023. "Higher-order beliefs in a Sequential Social Dilemma," Working Papers 356, University of California, Davis, Department of Economics.
    • Handle: RePEc:cda:wpaper:356
    as

    Download full text from publisher

    File URL: https://repec.dss.ucdavis.edu/files/Fx8UwGs6SG4rdamttQsuTgaD/Higher_order_beliefs_submit_to_IER.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Rutström, E. Elisabet & Wilcox, Nathaniel T., 2009. "Stated beliefs versus inferred beliefs: A methodological inquiry and experimental test," Games and Economic Behavior, Elsevier, vol. 67(2), pages 616-632, November.
    2. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    3. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    4. Andreoni, James & Rao, Justin M., 2011. "The power of asking: How communication affects selfishness, empathy, and altruism," Journal of Public Economics, Elsevier, vol. 95(7), pages 513-520.
    5. Vincent P. Crawford & Miguel A. Costa-Gomes & Nagore Iriberri, 2013. "Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications," Journal of Economic Literature, American Economic Association, vol. 51(1), pages 5-62, March.
    6. Goeree, Jacob K. & Holt, Charles A. & Palfrey, Thomas R., 2002. "Quantal Response Equilibrium and Overbidding in Private-Value Auctions," Journal of Economic Theory, Elsevier, vol. 104(1), pages 247-272, May.
    7. Vincent P. Crawford & Miguel A. Costa-Gomes, 2006. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 96(5), pages 1737-1768, December.
    8. 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.
    9. Frechette, Guillaume & Kagel, John H. & Morelli, Massimo, 2005. "Nominal bargaining power, selection protocol, and discounting in legislative bargaining," Journal of Public Economics, Elsevier, vol. 89(8), pages 1497-1517, August.
    10. Cooper, Russell & DeJong, Douglas V. & Forsythe, Robert & Ross, Thomas W., 1996. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Games and Economic Behavior, Elsevier, vol. 12(2), pages 187-218, February.
    11. Khalmetski, Kiryl & Ockenfels, Axel & Werner, Peter, 2015. "Surprising gifts: Theory and laboratory evidence," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 163-208.
    12. Chen, Daniel L. & Schonger, Martin & Wickens, Chris, 2016. "oTree—An open-source platform for laboratory, online, and field experiments," Journal of Behavioral and Experimental Finance, Elsevier, vol. 9(C), pages 88-97.
    13. Andreoni, James A & Miller, John H, 1993. "Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence," Economic Journal, Royal Economic Society, vol. 103(418), pages 570-585, May.
    14. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 9-41, June.
    15. Evan M. Calford & Anujit Chakraborty, 2020. "The Network Dilemma," Purdue University Economics Working Papers 1323, Purdue University, Department of Economics.
    16. Gary Charness & Martin Dufwenberg, 2006. "Promises and Partnership," Econometrica, Econometric Society, vol. 74(6), pages 1579-1601, November.
    17. Rosenthal, Robert W., 1981. "Games of perfect information, predatory pricing and the chain-store paradox," Journal of Economic Theory, Elsevier, vol. 25(1), pages 92-100, August.
    18. David Danz & Lise Vesterlund & Alistair J. Wilson, 2022. "Belief Elicitation and Behavioral Incentive Compatibility," American Economic Review, American Economic Association, vol. 112(9), pages 2851-2883, September.
    19. Kneeland, Terri, 2016. "Coordination under limited depth of reasoning," Games and Economic Behavior, Elsevier, vol. 96(C), pages 49-64.
    20. Dufwenberg, Martin & Van Essen, Matt, 2018. "King of the Hill: Giving backward induction its best shot," Games and Economic Behavior, Elsevier, vol. 112(C), pages 125-138.
    21. Ellingsen, Tore & Johannesson, Magnus & Tjøtta, Sigve & Torsvik, Gaute, 2010. "Testing guilt aversion," Games and Economic Behavior, Elsevier, vol. 68(1), pages 95-107, January.
    22. Simon Gächter & Elke Renner, 2010. "The effects of (incentivized) belief elicitation in public goods experiments," Experimental Economics, Springer;Economic Science Association, vol. 13(3), pages 364-377, September.
    23. David Danz & Lise Vesterlund & Alistair J. Wilson, 2020. "Belief Elicitation: Limiting Truth Telling with Information on Incentives," NBER Working Papers 27327, National Bureau of Economic Research, Inc.
    24. Steven J. Bosworth, 2017. "The importance of higher-order beliefs to successful coordination," Experimental Economics, Springer;Economic Science Association, vol. 20(1), pages 237-258, March.
    25. Agranov, Marina & Tergiman, Chloe, 2014. "Communication in multilateral bargaining," Journal of Public Economics, Elsevier, vol. 118(C), pages 75-85.
    26. Frã‰Chette, Guillaume R. & Kagel, John H. & Lehrer, Steven F., 2003. "Bargaining in Legislatures: An Experimental Investigation of Open versus Closed Amendment Rules," American Political Science Review, Cambridge University Press, vol. 97(2), pages 221-232, May.
    27. Charness, Gary & Dufwenberg, Martin, 2003. "Promises & Partnership," Research Papers in Economics 2003:3, Stockholm University, Department of Economics.
    28. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. García-Pola, Bernardo & Iriberri, Nagore & Kovářík, Jaromír, 2020. "Non-equilibrium play in centipede games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 391-433.
    2. Choo, Lawrence C.Y & Kaplan, Todd R., 2014. "Explaining Behavior in the "11-20" Game," MPRA Paper 52808, University Library of Munich, Germany.
    3. Jensen, Martin Kaae & Kozlovskaya, Maria, 2016. "A representation theorem for guilt aversion," Journal of Economic Behavior & Organization, Elsevier, vol. 125(C), pages 148-161.
    4. Baron, David P. & Bowen, T. Renee & Nunnari, Salvatore, 2017. "Durable coalitions and communication: Public versus private negotiations," Journal of Public Economics, Elsevier, vol. 156(C), pages 1-13.
    5. 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.
    6. Andrzej Baranski & Caleb A. Cox, 2023. "Communication in multilateral bargaining with joint production," Experimental Economics, Springer;Economic Science Association, vol. 26(1), pages 55-77, March.
    7. Nunnari, Salvatore & Zapal, Jan, 2016. "Gambler's fallacy and imperfect best response in legislative bargaining," Games and Economic Behavior, Elsevier, vol. 99(C), pages 275-294.
    8. Breitmoser, Yves & Tan, Jonathan H.W. & Zizzo, Daniel John, 2014. "On the beliefs off the path: Equilibrium refinement due to quantal response and level-k," Games and Economic Behavior, Elsevier, vol. 86(C), pages 102-125.
    9. Marco Battaglini & Thomas Palfrey, 2012. "The dynamics of distributive politics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(3), pages 739-777, April.
    10. Dan Levin & Luyao Zhang, 2022. "Bridging Level-K to Nash Equilibrium," Papers 2202.12292, arXiv.org, revised Feb 2022.
    11. Camerer, Colin F. & Ho, Teck-Hua, 2015. "Behavioral Game Theory Experiments and Modeling," Handbook of Game Theory with Economic Applications,, Elsevier.
    12. Ye Jin, 2021. "Does level-k behavior imply level-k thinking?," Experimental Economics, Springer;Economic Science Association, vol. 24(1), pages 330-353, March.
    13. Kyle Hyndman & Antoine Terracol & Jonathan Vaksmann, 2022. "Beliefs and (in)stability in normal-form games," Experimental Economics, Springer;Economic Science Association, vol. 25(4), pages 1146-1172, September.
    14. Breitmoser, Yves, 2019. "Knowing me, imagining you: Projection and overbidding in auctions," Games and Economic Behavior, Elsevier, vol. 113(C), pages 423-447.
    15. 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.
    16. Nagel, Rosemarie & Bühren, Christoph & Frank, Björn, 2017. "Inspired and inspiring: Hervé Moulin and the discovery of the beauty contest game," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 191-207.
    17. Charness, Gary & Gneezy, Uri & Rasocha, Vlastimil, 2021. "Experimental methods: Eliciting beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 189(C), pages 234-256.
    18. Penczynski, Stefan P., 2017. "The nature of social learning: Experimental evidence," European Economic Review, Elsevier, vol. 94(C), pages 148-165.
    19. Syngjoo Choi, 2012. "A cognitive hierarchy model of learning in networks," Review of Economic Design, Springer;Society for Economic Design, vol. 16(2), pages 215-250, September.
    20. Vittorio Pelligra & Tommaso Reggiani & Daniel John Zizzo, 2020. "Responding to (un)reasonable requests by an authority," Theory and Decision, Springer, vol. 89(3), pages 287-311, October.

    More about this item

    JEL classification:

    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cda:wpaper:356. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Letters and Science IT Services Unit (email available below). General contact details of provider: https://edirc.repec.org/data/educdus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.