IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpex/0110003.html
   My bibliography  Save this paper

Choice of Prizes Allocated by Multiple Lotteries with Endogenously Determined Probabilities

Author

Listed:
  • Amnon Rapoport

    (University of Arizona)

  • Alison King Chung Lo

    (Duke University)

  • Rami Zwick

    (The Hong Kong University of Science and Technology)

Abstract

We study a class of interactive decision making situations in which each agent must choose to participate in one of several lotteries with commonly known prizes. In contrast to the widely studied paradigm of choice between gambles in individual decision making under risk, the probability of winning a prize in each of the lotteries in our study is endogenously determined. In particular, for each lottery, it is known to decrease in the number of agents choosing to play that lottery. We construct the Nash equilibrium solution to this game and then test it experimentally in the special case where each lottery yields only a single prize. The results show a remarkable degree of tacit coordination that supports the equilibrium solution under the assumption of common risk-aversion. However, this coordination is not achieved via individual level randomization. Rather, the entry decisions of most of the subjects can be characterized by local adjustments to the outcome of the previous iteration of the same game along the lines suggested by anticipatory learning models.

Suggested Citation

  • Amnon Rapoport & Alison King Chung Lo & Rami Zwick, 2001. "Choice of Prizes Allocated by Multiple Lotteries with Endogenously Determined Probabilities," Experimental 0110003, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpex:0110003
    Note: Type of Document - Acrobat PDF; prepared on PC; pages: 42; figures: included
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/exp/papers/0110/0110003.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. 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.
    3. Kahneman, Daniel & Knetsch, Jack L & Thaler, Richard H, 1986. "Fairness and the Assumptions of Economics," The Journal of Business, University of Chicago Press, vol. 59(4), pages 285-300, October.
    4. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    5. Wu, George & Gonzalez, Richard, 1998. "Common Consequence Conditions in Decision Making under Risk," Journal of Risk and Uncertainty, Springer, vol. 16(1), pages 115-139, April.
    6. Amos Tversky & Daniel Kahneman, 1991. "Loss Aversion in Riskless Choice: A Reference-Dependent Model," The Quarterly Journal of Economics, Oxford University Press, vol. 106(4), pages 1039-1061.
    7. Harrison, Glenn W, 1989. "Theory and Misbehavior of First-Price Auctions," American Economic Review, American Economic Association, vol. 79(4), pages 749-762, September.
    8. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
    9. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    10. Ho, Teck-Hua & Camerer, Colin & Weigelt, Keith, 1998. "Iterated Dominance and Iterated Best Response in Experimental "p-Beauty Contests."," American Economic Review, American Economic Association, vol. 88(4), pages 947-969, September.
    11. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945.
    12. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-196, March.
    13. Smith, Vernon L, 1985. "Experimental Economics: Reply," American Economic Review, American Economic Association, vol. 75(1), pages 264-272, March.
    14. Friedman, Daniel, 1992. "Theory and Misbehavior of First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1374-1378, December.
    15. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    16. Merlo, Antonio & Schotter, Andrew, 1992. "Theory and Misbehavior of First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1413-1425, December.
    17. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    18. 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.
    19. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    20. Pamela K. Lattimore & Joanna R. Baker & A. Dryden Witte, 1992. "The Influence Of Probability on Risky Choice: A parametric Examination," NBER Technical Working Papers 0081, National Bureau of Economic Research, Inc.
    21. Kagel, John H & Roth, Alvin E, 1992. "Theory and Misbehavior in First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1379-1391, December.
    22. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
    23. Cox, James C & Smith, Vernon L & Walker, James M, 1992. "Theory and Misbehavior of First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1392-1412, December.
    24. 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.
    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. Rami Zwick & Amnon Rapoport & Alison King Chung Lo, 2001. "Behavioral Strategies in Repeated Pure Coordination Games," Experimental 0110004, University Library of Munich, Germany.
    2. Blume, A. & DeJong, D.V. & Maier, M., 2005. "Cognition in Spatial Dispersion Games," Other publications TiSEM facac215-420c-4a02-b2f3-e, Tilburg University, School of Economics and Management.
    3. Yoder, Jonathan K. & Ohler, Adrienne M. & Chouinard, Hayley H., 2014. "What floats your boat? Preference revelation from lotteries over complex goods," Journal of Environmental Economics and Management, Elsevier, vol. 67(3), pages 412-430.
    4. Blume, A. & DeJong, D.V. & Maier, M., 2005. "Cognition in Spatial Dispersion Games," Discussion Paper 2005-58, Tilburg University, Center for Economic Research.
    5. Yu Wang & Ernan Haruvy, 2013. "Tiers in One-Sided Matching Markets: Theory and Experimental Investigation," Management Science, INFORMS, vol. 59(6), pages 1458-1477, June.
    6. Anna Dorfman & Yoella Bereby-Meyer & Simone Moran, 2013. "When Feeling Skillful Impairs Coordination in a Lottery Selection Task," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-6, June.

    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. Jinkwon Lee, 2007. "Repetition And Financial Incentives In Economics Experiments," Journal of Economic Surveys, Wiley Blackwell, vol. 21(3), pages 628-681, July.
    2. Erel Avineri, 2006. "The Effect of Reference Point on Stochastic Network Equilibrium," Transportation Science, INFORMS, vol. 40(4), pages 409-420, November.
    3. 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.
    4. 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.
    5. Jay R. Corrigan & Matthew C. Rousu, 2006. "The Effect of Initial Endowments in Experimental Auctions," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 88(2), pages 448-457.
    6. Eyal Baharad & Doron Kliger, 2013. "Market failure in light of non-expected utility," Theory and Decision, Springer, vol. 75(4), pages 599-619, October.
    7. Özalp Özer & Yanchong Zheng, 2016. "Markdown or Everyday Low Price? The Role of Behavioral Motives," Management Science, INFORMS, vol. 62(2), pages 326-346, February.
    8. Daniel Cavagnaro & Mark Pitt & Richard Gonzalez & Jay Myung, 2013. "Discriminating among probability weighting functions using adaptive design optimization," Journal of Risk and Uncertainty, Springer, vol. 47(3), pages 255-289, December.
    9. Willemien Kets, 2007. "The minority game: An economics perspective," Papers 0706.4432, arXiv.org.
    10. Ajay Kalra & Mengze Shi, 2002. "Consumer Value-Maximizing Sweepstakes & Contests: A Theoretical and Experimental Investigation," Review of Marketing Science Working Papers 1-3-1008, Berkeley Electronic Press.
    11. José Lara Resende & George Wu, 2010. "Competence effects for choices involving gains and losses," Journal of Risk and Uncertainty, Springer, vol. 40(2), pages 109-132, April.
    12. 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.
    13. Fiore, Annamaria, 2009. "Experimental Economics: Some Methodological Notes," MPRA Paper 12498, University Library of Munich, Germany.
    14. Horst Zank, 2010. "On probabilities and loss aversion," Theory and Decision, Springer, vol. 68(3), pages 243-261, March.
    15. George Wu & Richard Gonzalez, 1999. "Nonlinear Decision Weights in Choice Under Uncertainty," Management Science, INFORMS, vol. 45(1), pages 74-85, January.
    16. Davies, G.B. & Satchell, S.E., 2004. "Continuous Cumulative Prospect Theory and Individual Asset Allocation," Cambridge Working Papers in Economics 0467, Faculty of Economics, University of Cambridge.
    17. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
    18. Olivier Armantier & Nicolas Treich, 2006. "Overbidding in Independant Private-Values Auctions and Misperception of Probabilities," CIRANO Working Papers 2006s-15, CIRANO.
    19. Foster, Gigi & Frijters, Paul & Schaffner, Markus & Torgler, Benno, 2018. "Expectation formation in an evolving game of uncertainty: New experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 154(C), pages 379-405.
    20. Kerim Keskin, 2016. "Inverse S-shaped probability weighting functions in first-price sealed-bid auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 20(1), pages 57-67, March.

    More about this item

    Keywords

    Coordination; Endogenously Determined Probabilities;

    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

    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:wpa:wuwpex:0110003. 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://econwpa.ub.uni-muenchen.de .

    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: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    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.