IDEAS home Printed from https://ideas.repec.org/p/usg/econwp/201207.html
   My bibliography  Save this paper

Eliciting Beliefs in Continuous-Choice Games: A Double Auction Experiment

Author

Listed:
  • Neri, Claudia

Abstract

This paper proposes a methodology to implement probabilistic belief elicitation in continuous-choice games. Representing subjective probabilistic beliefs about a continuous variable as a continuous subjective probability distribution, the methodology involves eliciting partial information about the subjective distribution and fitting a parametric distribution on the elicited data. As an illustration, the methodology is applied to a double auction experiment, where traders' beliefs about the bidding choices of other market participants are elicited. Elicited subjective beliefs are found to differ from proxies such as Bayesian Nash Equilibrium (BNE) beliefs and empirical beliefs, both in terms of the forecasts of other traders' bidding choices and in terms of the best-response bidding choices prescribed by beliefs. Elicited subjective beliefs help explain observed bidding choices better than BNE beliefs and empirical beliefs. By extending probabilistic belief elicitation beyond discrete-choice games to continuous-choice games, the proposed methodology enables to investigate the role of beliefs in a wider range of applications.

Suggested Citation

  • Neri, Claudia, 2012. "Eliciting Beliefs in Continuous-Choice Games: A Double Auction Experiment," Economics Working Paper Series 1207, University of St. Gallen, School of Economics and Political Science, revised Dec 2012.
  • Handle: RePEc:usg:econwp:2012:07
    as

    Download full text from publisher

    File URL: http://ux-tauri.unisg.ch/RePEc/usg/econwp/EWP-1207.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. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    3. Charles Bellemare & Alexander Sebald & Martin Strobel, 2011. "Measuring the willingness to pay to avoid guilt: estimation using equilibrium and stated belief models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(3), pages 437-453, April.
    4. Miguel A. Costa-Gomes & Georg Weizsäcker, 2008. "Stated Beliefs and Play in Normal-Form Games," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 729-762.
    5. Palfrey, Thomas R. & Wang, Stephanie W., 2009. "On eliciting beliefs in strategic games," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 98-109, August.
    6. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    7. David Danz & Dietmar Fehr & Dorothea Kübler, 2012. "Information and beliefs in a repeated normal-form game," Experimental Economics, Springer;Economic Science Association, vol. 15(4), pages 622-640, December.
    8. Ernan Haruvy & Yaron Lahav & Charles N. Noussair, 2007. "Traders' Expectations in Asset Markets: Experimental Evidence," American Economic Review, American Economic Association, vol. 97(5), pages 1901-1920, December.
    9. Urs Fischbacher, 2007. "z-Tree: Zurich toolbox for ready-made economic experiments," Experimental Economics, Springer;Economic Science Association, vol. 10(2), pages 171-178, June.
    10. Manski, Charles F. & Neri, Claudia, 2013. "First- and second-order subjective expectations in strategic decision-making: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 232-254.
    11. Timothy N. Cason & Daniel Friedman, 1997. "Price Formation in Single Call Markets," Econometrica, Econometric Society, vol. 65(2), pages 311-346, March.
    12. J. Dominitz & C. F. Manski, "undated". "Using expectations data to study subjective income expectations," Institute for Research on Poverty Discussion Papers 1050-94, University of Wisconsin Institute for Research on Poverty.
    13. repec:taf:jnlbes:v:30:y:2012:i:1:p:125-131 is not listed on IDEAS
    14. Cheung, Yin-Wong & Friedman, Daniel, 1997. "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, Elsevier, vol. 19(1), pages 46-76, April.
    15. Sonnemans, Joep & Hommes, Cars & Tuinstra, Jan & van de Velden, Henk, 2004. "The instability of a heterogeneous cobweb economy: a strategy experiment on expectation formation," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 453-481, August.
    16. Rey-Biel, Pedro, 2009. "Equilibrium play and best response to (stated) beliefs in normal form games," Games and Economic Behavior, Elsevier, vol. 65(2), pages 572-585, March.
    17. Charles Bellemare & Luc Bissonnette & Sabine Kröger, 2011. "Flexible Approximation of Subjective Expectations Using Probability Questions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 125-131, April.
    18. Rustichini, Aldo & Satterthwaite, Mark A & Williams, Steven R, 1994. "Convergence to Efficiency in a Simple Market with Incomplete Information," Econometrica, Econometric Society, vol. 62(5), pages 1041-1063, September.
    19. Armantier, Olivier & Treich, Nicolas, 2013. "Eliciting beliefs: Proper scoring rules, incentives, stakes and hedging," European Economic Review, Elsevier, vol. 62(C), pages 17-40.
    20. Olivier Armantier & Nicolas Treich, 2009. "Subjective Probabilities In Games: An Application To The Overbidding Puzzle," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(4), pages 1079-1102, November.
    21. Mariana Blanco & Dirk Engelmann & Alexander Koch & Hans-Theo Normann, 2010. "Belief elicitation in experiments: is there a hedging problem?," Experimental Economics, Springer;Economic Science Association, vol. 13(4), pages 412-438, December.
    22. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    23. Engelberg, Joseph & Manski, Charles F. & Williams, Jared, 2009. "Comparing the Point Predictions and Subjective Probability Distributions of Professional Forecasters," Journal of Business & Economic Statistics, American Statistical Association, vol. 27, pages 30-41.
    24. Colin Camerer & Teck H Ho & Juin-Kuan Chong & Keith Weigelt, 2003. "Strategic teaching and equilibrium models of repeated trust and entry games," Levine's Bibliography 506439000000000506, UCLA Department of Economics.
    25. Charles F. Manski, 2004. "Measuring Expectations," Econometrica, Econometric Society, vol. 72(5), pages 1329-1376, September.
    26. Manski, Charles F., 2002. "Identification of decision rules in experiments on simple games of proposal and response," European Economic Review, Elsevier, vol. 46(4-5), pages 880-891, May.
    27. Cars Hommes & Joep Sonnemans & Jan Tuinstra & Henk van de Velden, 2005. "Coordination of Expectations in Asset Pricing Experiments," Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 955-980.
    28. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945.
    29. Smith, Vernon L & Suchanek, Gerry L & Williams, Arlington W, 1988. "Bubbles, Crashes, and Endogenous Expectations in Experimental Spot Asset Markets," Econometrica, Econometric Society, vol. 56(5), pages 1119-1151, September.
    30. Yaw Nyarko & Andrew Schotter, 2002. "An Experimental Study of Belief Learning Using Elicited Beliefs," Econometrica, Econometric Society, vol. 70(3), pages 971-1005, May.
    31. Oliver Kirchkamp & J. Philipp Reiß, 2011. "Out‐Of‐Equilibrium Bids in First‐Price Auctions: Wrong Expectations or Wrong Bids," Economic Journal, Royal Economic Society, vol. 121(557), pages 1361-1397, December.
    32. Kyle Hyndman & Erkut Y. Ozbay & Andrew Schotter & Wolf Ze’ev Ehrblatt, 2012. "Convergence: An Experimental Study Of Teaching And Learning In Repeated Games," Journal of the European Economic Association, European Economic Association, vol. 10(3), pages 573-604, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Charles Bellemare & Sabine Kröger & Kouamé Marius Sossou, 2018. "Reporting probabilistic expectations with dynamic uncertainty about possible distributions," Journal of Risk and Uncertainty, Springer, vol. 57(2), pages 153-176, October.
    2. Chen, Si & Schildberg-Hörisch, Hannah, 2018. "Looking at the bright side: The motivation value of overconfidence," DICE Discussion Papers 291, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    3. Chen Li & Uyanga Turmunkh & Peter P. Wakker, 2019. "Trust as a decision under ambiguity," Experimental Economics, Springer;Economic Science Association, vol. 22(1), pages 51-75, March.
    4. Markus Eyting & Patrick Schmidt, 2019. "Belief Elicitation with Multiple Point Predictions," Working Papers 1818, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 16 Nov 2020.
    5. Eyting, Markus & Schmidt, Patrick, 2021. "Belief elicitation with multiple point predictions," European Economic Review, Elsevier, vol. 135(C).
    6. Claudia Neri, 2015. "Quantal response equilibrium in a double auction," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 79-90, April.
    7. Chen, Si & Schildberg-Hörisch, Hannah, 2019. "Looking at the bright side: The motivational value of confidence," European Economic Review, Elsevier, vol. 120(C).
    8. Sascha Füllbrunn & Tibor Neugebauer, 2013. "Varying the number of bidders in the first-price sealed-bid auction: experimental evidence for the one-shot game," Theory and Decision, Springer, vol. 75(3), pages 421-447, September.
    9. Polonio, Luca & Coricelli, Giorgio, 2019. "Testing the level of consistency between choices and beliefs in games using eye-tracking," Games and Economic Behavior, Elsevier, vol. 113(C), pages 566-586.

    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. Manski, Charles F. & Neri, Claudia, 2013. "First- and second-order subjective expectations in strategic decision-making: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 232-254.
    2. Folli, Dominik & Wolff, Irenaeus, 2022. "Biases in belief reports," Journal of Economic Psychology, Elsevier, vol. 88(C).
    3. Polonio, Luca & Coricelli, Giorgio, 2019. "Testing the level of consistency between choices and beliefs in games using eye-tracking," Games and Economic Behavior, Elsevier, vol. 113(C), pages 566-586.
    4. Charness, Gary & Gneezy, Uri & Rasocha, Vlastimil, 2021. "Experimental methods: Eliciting beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 189(C), pages 234-256.
    5. Dominik Bauer & Irenaeus Wolff, 2018. "Biases in Beliefs: Experimental Evidence," TWI Research Paper Series 109, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
    6. Bauer, Dominik & Wolff, Irenaeus, 2019. "Biases in Beliefs," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203601, Verein für Socialpolitik / German Economic Association.
    7. 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.
    8. Armantier, Olivier & Treich, Nicolas, 2013. "Eliciting beliefs: Proper scoring rules, incentives, stakes and hedging," European Economic Review, Elsevier, vol. 62(C), pages 17-40.
    9. Eyting, Markus & Schmidt, Patrick, 2021. "Belief elicitation with multiple point predictions," European Economic Review, Elsevier, vol. 135(C).
    10. Rutstrom, E. Elizabet & Wilcox, Nathaniel, 2008. "Stated versus inferred beliefs: A methodological inquiry and experimental test," MPRA Paper 11852, University Library of Munich, Germany.
    11. Alex Possajennikov, 2018. "Belief formation in a signaling game without common prior: an experiment," Theory and Decision, Springer, vol. 84(3), pages 483-505, May.
    12. Stefan T. Trautmann & Gijs Kuilen, 2015. "Belief Elicitation: A Horse Race among Truth Serums," Economic Journal, Royal Economic Society, vol. 125(589), pages 2116-2135, December.
    13. Cason, Timothy N. & Friedman, Daniel & Hopkins, Ed, 2010. "Testing the TASP: An experimental investigation of learning in games with unstable equilibria," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2309-2331, November.
    14. Haruvy, Ernan & Stahl, Dale O., 2012. "Between-game rule learning in dissimilar symmetric normal-form games," Games and Economic Behavior, Elsevier, vol. 74(1), pages 208-221.
    15. Karl Schlag & James Tremewan & Joël Weele, 2015. "A penny for your thoughts: a survey of methods for eliciting beliefs," Experimental Economics, Springer;Economic Science Association, vol. 18(3), pages 457-490, September.
    16. Maoliang Ye & Jie Zheng & Plamen Nikolov & Sam Asher, 2020. "One Step at a Time: Does Gradualism Build Coordination?," Management Science, INFORMS, vol. 66(1), pages 113-129, January.
    17. Wen, Yuanji, 2018. "Voluntary information acquisition in an asymmetric-Information game:comparing learning theories in the laboratory," Journal of Economic Behavior & Organization, Elsevier, vol. 150(C), pages 202-219.
    18. David Danz & Dietmar Fehr & Dorothea Kübler, 2012. "Information and beliefs in a repeated normal-form game," Experimental Economics, Springer;Economic Science Association, vol. 15(4), pages 622-640, December.
    19. Victor Aguirregabiria & Jihye Jeon, 2020. "Firms’ Beliefs and Learning: Models, Identification, and Empirical Evidence," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 56(2), pages 203-235, March.
    20. Wolf Ze'ev Ehrblatt & Kyle Hyndman & Erkut Y. ÄOzbay & Andrew Schotter, 2006. "Convergence: An Experimental Study," Levine's Working Paper Archive 122247000000001148, David K. Levine.

    More about this item

    Keywords

    Probabilistic beliefs; subjective expectations; private information; experiments; auctions;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior

    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:usg:econwp:2012:07. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/vwasgch.html .

    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: (email available below). General contact details of provider: https://edirc.repec.org/data/vwasgch.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.