IDEAS home Printed from https://ideas.repec.org/p/ecm/wc2000/0222.html
   My bibliography  Save this paper

Third Down with a Yard to Go: The Dixit-Skeath Conundrum on Equilibria in Competitive Games

Author

Listed:
  • Simon Grant

    (Australian National University)

  • Atsushi Kajii

    (University of Tsukuba)

  • Ben Polak

    (Yale University)

Abstract

In strictly competitive games, equilibrium mixed strategies are invariant to changes in the ultimate prizes. Dixit and Skeath argue that this seems counter-intuitive, and it is a challenge to the expected utility theory. We show that this invariance is robust to dropping the independence axiom, but is removed if we drop the reduction axiom. The conditions on the resulting recursive expected-utility model to get the desired outcome are analogous to conditions used in the standard model of comparative statics under risk.

Suggested Citation

  • Simon Grant & Atsushi Kajii & Ben Polak, 2000. "Third Down with a Yard to Go: The Dixit-Skeath Conundrum on Equilibria in Competitive Games," Econometric Society World Congress 2000 Contributed Papers 0222, Econometric Society.
    • Handle: RePEc:ecm:wc2000:0222
    as

    Download full text from publisher

    File URL: http://fmwww.bc.edu/RePEc/es2000/0222.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Grant, Simon & Kajii, Atsushi & Polak, Ben, 1998. "Intrinsic Preference for Information," Journal of Economic Theory, Elsevier, vol. 83(2), pages 233-259, December.
    2. Gollier Christian, 1995. "The Comparative Statics of Changes in Risk Revisited," Journal of Economic Theory, Elsevier, vol. 66(2), pages 522-535, August.
    3. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
    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. Grant, Simon & Kajii, Atsushi & Polak, Ben, 2001. ""Third down with a yard to go": recursive expected utility and the Dixit-Skeath conundrum," Economics Letters, Elsevier, vol. 73(3), pages 275-286, December.
    2. Hoel, Michael & Iversen, Tor & Nilssen, Tore & Vislie, Jon, 2003. "Genetic testing and repulsion from chance," Memorandum 20/2003, Oslo University, Department of Economics.
    3. Bruno Bassan & Olivier Gossner & Marco Scarsini & Shmuel Zamir, 2003. "Positive value of information in games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 17-31, December.
    4. Botond Kőszegi, 2010. "Utility from anticipation and personal equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(3), pages 415-444, September.
    5. Gollier, Christian, 2018. "Stochastic volatility implies fourth-degree risk dominance: Applications to asset pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 95(C), pages 155-171.
    6. Larbi Alaoui, 2012. "The value of useless information," Economics Working Papers 1313, Department of Economics and Business, Universitat Pompeu Fabra.
    7. Mohammed Abdellaoui & Han Bleichrodt & Olivier l'Haridon & Corina Paraschiv, 2013. "Is There One Unifying Concept of Utility?An Experimental Comparison of Utility Under Risk and Utility Over Time," Management Science, INFORMS, vol. 59(9), pages 2153-2169, September.
    8. Alaoui, Larbi, 2008. "The value of useless information," MPRA Paper 11411, University Library of Munich, Germany.
    9. Hoel, Michael & Iversen, Tor & Nilssen, Tore & Vislie, Jon, 2006. "Genetic testing in competitive insurance markets with repulsion from chance: A welfare analysis," Journal of Health Economics, Elsevier, vol. 25(5), pages 847-860, September.
    10. David Dillenberger, 2008. "Preferences for One-Shot Resolution of Uncertainty and Allais-Type Behavior," PIER Working Paper Archive 08-036, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    11. Simon Grant & Atsushi Kajii & Ben Polak, 2000. "Preference for Information and Dynamic Consistency," Theory and Decision, Springer, vol. 48(3), pages 263-286, May.
    12. Eliaz, Kfir & Schotter, Andrew, 2010. "Paying for confidence: An experimental study of the demand for non-instrumental information," Games and Economic Behavior, Elsevier, vol. 70(2), pages 304-324, November.
    13. Ergin, Haluk & Gul, Faruk, 2009. "A theory of subjective compound lotteries," Journal of Economic Theory, Elsevier, vol. 144(3), pages 899-929, May.
    14. Chen, Zhuo, 2022. "Preference for hope: A behavioral definition," Economics Letters, Elsevier, vol. 221(C).
    15. Ali Lazrak, 2005. "Generalized stochastic differential utility and preference for information," Papers math/0503579, arXiv.org.
    16. Daniel Bennett & Stefan Bode & Maja Brydevall & Hayley Warren & Carsten Murawski, 2016. "Intrinsic Valuation of Information in Decision Making under Uncertainty," PLOS Computational Biology, Public Library of Science, vol. 12(7), pages 1-21, July.
    17. Alexander L. Brown & Hwagyun Kim, 2014. "Do Individuals Have Preferences Used in Macro-Finance Models? An Experimental Investigation," Management Science, INFORMS, vol. 60(4), pages 939-958, April.
    18. Rommeswinkel, Hendrik & Chang, Hung-Chi & Hsu, Wen-Tai, 2023. "Preference for Knowledge," Journal of Economic Theory, Elsevier, vol. 214(C).
    19. Li, Jian, 2020. "Preferences for partial information and ambiguity," Theoretical Economics, Econometric Society, vol. 15(3), July.
    20. Dillenberger, David, 2008. "Preferences for One-Shot Resolution of Uncertainty and Allais-Type Behavior," MPRA Paper 8342, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:ecm:wc2000:0222. 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: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.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.