IDEAS home Printed from https://ideas.repec.org/p/qut/auncer/2012_1.html
   My bibliography  Save this paper

μ-σ Games

Author

Listed:
  • Uwe Dulleck

    (QUT)

  • Andreas Loffler

Abstract

Risk aversion in game theory is usually modelled using expected utility, which has been critized early on leading to an extensive literature on generalized expected utility. In this paper we are first to apply μ-σ theory to the analysis of (static) games. μ-σ theory is widely accepted in the finance literature, using it allows us to study the effect on uncertainty endogenous to the game, i.e. mixed equilibria. In particular, we look at the case of linear μ-σ utility functions and determine the best response strategy. In the case of 2x2- and NxM-games we are able to characterize all mixed equilibria.

Suggested Citation

  • Uwe Dulleck & Andreas Loffler, 2012. "μ-σ Games," NCER Working Paper Series 78, National Centre for Econometric Research.
    • Handle: RePEc:qut:auncer:2012_1
    as

    Download full text from publisher

    File URL: http://www.ncer.edu.au/papers/documents/WP78.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    • Uwe Dulleck & Andreas Löffler, 2021. "μ – σ Games," Games, MDPI, vol. 12(1), pages 1-12, January.

    References listed on IDEAS

    as
    1. Fama, Eugene F & French, Kenneth R, 1992. "The Cross-Section of Expected Stock Returns," Journal of Finance, American Finance Association, vol. 47(2), pages 427-465, June.
    2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    3. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, vol. 50(1), pages 127-154, February.
    4. Fatma Lajeri-Chaherli, 2002. "More on Properness: The Case of Mean-Variance Preferences," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 27(1), pages 49-60, June.
    5. Eichberger, Jurgen & Kelsey, David, 1996. "Uncertainty Aversion and Preference for Randomisation," Journal of Economic Theory, Elsevier, vol. 71(1), pages 31-43, October.
    6. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    7. Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175-202, February.
    8. Lars Tyge Nielsen & Fatma Lajeri, 2000. "Parametric characterizations of risk aversion and prudence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 469-476.
    9. Battigalli, Pierpaolo & Dufwenberg, Martin, 2009. "Dynamic psychological games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 1-35, January.
    10. Battalio, Raymond & Samuelson, Larry & Van Huyck, John, 2001. "Optimization Incentives and Coordination Failure in Laboratory Stag Hunt Games," Econometrica, Econometric Society, vol. 69(3), pages 749-764, May.
    11. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    12. Ho-Chyuan Chen & William Neilson, 1999. "Pure-strategy Equilibria with Non-expected Utility Players," Theory and Decision, Springer, vol. 46(2), pages 201-212, April.
    13. Daniel Ellsberg, 1963. "Risk, Ambiguity, and the Savage Axioms: Reply," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 77(2), pages 336-342.
    14. Howard Raiffa, 1961. "Risk, Ambiguity, and the Savage Axioms: Comment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 690-694.
    15. Nielsen, Lars Tyge, 1987. "Portfolio Selection in the Mean-Variance Model: A Note," Journal of Finance, American Finance Association, vol. 42(5), pages 1371-1376, December.
    16. Geanakoplos, John & Pearce, David & Stacchetti, Ennio, 1989. "Psychological games and sequential rationality," Games and Economic Behavior, Elsevier, vol. 1(1), pages 60-79, March.
    17. Meyer, Jack, 1987. "Two-moment Decision Models and Expected Utility Maximization," American Economic Review, American Economic Association, vol. 77(3), pages 421-430, June.
    18. Rabin, Matthew, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December.
    19. Dekel, Eddie & Safra, Zvi & Segal, Uzi, 1991. "Existence and dynamic consistency of Nash equilibrium with non-expected utility preferences," Journal of Economic Theory, Elsevier, vol. 55(2), pages 229-246, December.
    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. van Damme, Eric & Binmore, Kenneth G. & Roth, Alvin E. & Samuelson, Larry & Winter, Eyal & Bolton, Gary E. & Ockenfels, Axel & Dufwenberg, Martin & Kirchsteiger, Georg & Gneezy, Uri & Kocher, Martin G, 2014. "How Werner Güth's ultimatum game shaped our understanding of social behavior," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 292-318.
    2. Sawa, Ryoji & Wu, Jiabin, 2018. "Prospect dynamics and loss dominance," Games and Economic Behavior, Elsevier, vol. 112(C), pages 98-124.
    3. Dufwenberg, Martin & Gächter, Simon & Hennig-Schmidt, Heike, 2011. "The framing of games and the psychology of play," Games and Economic Behavior, Elsevier, vol. 73(2), pages 459-478.
    4. Marcello Basili & Carlo Zappia, 2010. "Ambiguity and uncertainty in Ellsberg and Shackle," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 34(3), pages 449-474.
    5. Wing-Keung Wong & Chenghu Ma, 2008. "Preferences over location-scale family," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 37(1), pages 119-146, October.
    6. Martin Dufwenberg & Simon Gaechter & Heike Hennig-Schmidt, 2006. "The Framing of Games and the Psychology of Strategic Choice," Discussion Papers 2006-20, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    7. Belianin, A., 2017. "Face to Face to Human Being: Achievements and Challenges of Behavioral Economics," Journal of the New Economic Association, New Economic Association, vol. 34(2), pages 166-175.
    8. Marc Willinger, 1990. "La rénovation des fondements de l'utilité et du risque," Revue Économique, Programme National Persée, vol. 41(1), pages 5-48.
    9. Dorian Beauchêne, 2016. "Solution concepts for games with ambiguous payoffs," Theory and Decision, Springer, vol. 80(2), pages 245-269, February.
    10. Rindone, Fabio & Greco, Salvatore & Di Gaetano, Luigi, 2013. "On prospects and games: an equilibrium analysis under prospect theory," MPRA Paper 52131, University Library of Munich, Germany.
    11. Dufwenberg, Martin & Gächter, Simon & Hennig-Schmidt, Heike, 2011. "The framing of games and the psychology of play," Games and Economic Behavior, Elsevier, vol. 73(2), pages 459-478.
    12. Upravitelev, A., 2023. "Neoclassical roots of behavioral economics," Journal of the New Economic Association, New Economic Association, vol. 58(1), pages 110-140.
    13. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    14. Ederer, Florian & Stremitzer, Alexander, 2017. "Promises and expectations," Games and Economic Behavior, Elsevier, vol. 106(C), pages 161-178.
    15. Dufwenberg, Martin & Patel, Amrish, 2019. "Introduction to special issue on psychological game theory," Journal of Economic Behavior & Organization, Elsevier, vol. 167(C), pages 181-184.
    16. Jiabin Wu, 2018. "Indirect higher order beliefs and cooperation," Experimental Economics, Springer;Economic Science Association, vol. 21(4), pages 858-876, December.
    17. von Siemens, Ferdinand A., 2013. "Intention-based reciprocity and the hidden costs of control," Journal of Economic Behavior & Organization, Elsevier, vol. 92(C), pages 55-65.
    18. Mohammed Abdellaoui & Horst Zank, 2023. "Source and rank-dependent utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(4), pages 949-981, May.
    19. Dufwenberg, Martin & Patel, Amrish, 2017. "Reciprocity networks and the participation problem," Games and Economic Behavior, Elsevier, vol. 101(C), pages 260-272.
    20. Epper, Thomas & Fehr-Duda, Helga, 2017. "A Tale of Two Tails: On the Coexistence of Overweighting and Underweighting of Rare Extreme Events," Economics Working Paper Series 1705, University of St. Gallen, School of Economics and Political Science.

    More about this item

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    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:qut:auncer:2012_1. 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: School of Economics and Finance (email available below). General contact details of provider: https://edirc.repec.org/data/ncerrau.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.