IDEAS home Printed from https://ideas.repec.org/p/man/sespap/1503.html
   My bibliography  Save this paper

Piecewise Additivity for Nonexpected Utility

Author

Listed:
  • Craig S. Webb

Abstract

A model of choice under purely subjective uncertainty, Piecewise Additive Choquet Expected utility, is introduced. PACE utility allows for optimism and pessimism simultaneously, but represents a minimal departure from expected utility. It can be seen as a continuous version of NEO-expected utility (Chateauneuf et al. in J Econ Theory 137:538–567, 2007 ) and, as such, is especially suited for applications with rich state spaces. The main theorem provides a preference foundation for PACE utility in the Savage framework of purely subjective uncertainty with an arbitrary outcome set. Copyright Springer-Verlag Berlin Heidelberg 2015
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Craig S. Webb, 2015. "Piecewise Additivity for Nonexpected Utility," Economics Discussion Paper Series 1503, Economics, The University of Manchester.
    • Handle: RePEc:man:sespap:1503
    as

    Download full text from publisher

    File URL: https://hummedia.manchester.ac.uk/schools/soss/economics/discussionpapers/EDP-1503.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Itzhak Gilboa, 1988. "A Combination of Expected Utility and Maxmin Decision Criteria," Post-Print hal-00753244, HAL.
    2. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-1059, July.
    3. Ludwig, Alexander & Zimper, Alexander, 2014. "Biased Bayesian learning with an application to the risk-free rate puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 79-97.
    4. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
    5. Johannes W. Fedderke & Yang Liu, 2015. "Accounting for Productivity Growth: Schumpeterian versus Semi-Endogenous Explanantions," Working Papers 554, Economic Research Southern Africa.
    6. Eichberger, Jürgen & Grant, Simon & Lefort, Jean-Philippe, 2008. "Neo-additive capacities and updating," Papers 08-31, Sonderforschungsbreich 504.
    7. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
    8. Jürgen Eichberger & David Kelsey, 2014. "Optimism And Pessimism In Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(2), pages 483-505, May.
    9. repec:dau:papers:123456789/7604 is not listed on IDEAS
    10. Dominiak, Adam & Eichberger, Jürgen & Lefort, Jean-Philippe, 2012. "Agreeable trade with optimism and pessimism," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 119-126.
    11. Mohammed Abdellaoui & Aurelien Baillon & Laetitia Placido & Peter P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," American Economic Review, American Economic Association, vol. 101(2), pages 695-723, April.
    12. Jürgen Eichberger & David Kelsey, 2014. "Optimism And Pessimism In Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 483-505, May.
    13. Jürgen Eichberger & Simon Grant & Jean-Philippe Lefort, 2012. "Generalized neo-additive capacities and updating," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(3), pages 237-257, September.
    14. repec:cup:judgdm:v:9:y:2014:i:5:p:387-402 is not listed on IDEAS
    15. Craig R. Fox & Amos Tversky, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(3), pages 585-603.
    16. J L Ford & David Kelsey & W Pang, 2005. "Ambiguity in Financial Markets: Herding and Contrarian Behaviour," Discussion Papers 05-11, Department of Economics, University of Birmingham.
    17. Jürgen Eichberger & David Kelsey, 2011. "Are the treasures of game theory ambiguous?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 313-339, October.
    18. repec:dau:papers:123456789/7332 is not listed on IDEAS
    19. Wakker, Peter P., 2005. "Decision-foundations for properties of nonadditive measures: general state spaces or general outcome spaces," Games and Economic Behavior, Elsevier, vol. 50(1), pages 107-125, January.
    20. Chow, Clare Chua & Sarin, Rakesh K, 2001. "Comparative Ignorance and the Ellsberg Paradox," Journal of Risk and Uncertainty, Springer, vol. 22(2), pages 129-139, March.
    21. Chew, Soo Hong & Sagi, Jacob S., 2008. "Small worlds: Modeling attitudes toward sources of uncertainty," Journal of Economic Theory, Elsevier, vol. 139(1), pages 1-24, March.
    22. Wakker, Peter, 1989. "Continuous subjective expected utility with non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 1-27, February.
    23. Wakker, Peter, 1996. "The sure-thing principle and the comonotonic sure-thing principle: An axiomatic analysis," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 213-227.
    24. Mohammed Abdellaoui & Peter Wakker, 2005. "The Likelihood Method for Decision under Uncertainty," Theory and Decision, Springer, vol. 58(1), pages 3-76, February.
    25. Alain Chateauneuf & Fabio Maccheroni & Massimo Marinacci & Jean-Marc Tallon, 2005. "Monotone continuous multiple priors," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 973-982, November.
    26. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 1897-1908, November.
    27. Webb, Craig S. & Zank, Horst, 2011. "Accounting for optimism and pessimism in expected utility," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 706-717.
    28. Mohammed Abdellaoui & Olivier L’Haridon & Horst Zank, 2010. "Separating curvature and elevation: A parametric probability weighting function," Journal of Risk and Uncertainty, Springer, vol. 41(1), pages 39-65, August.
    29. Joshua C. Teitelbaum, 2007. "A Unilateral Accident Model under Ambiguity," The Journal of Legal Studies, University of Chicago Press, vol. 36(2), pages 431-477, June.
    30. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    31. repec:dau:papers:123456789/8588 is not listed on IDEAS
    32. Adam Dominiak & Jean-Philippe Lefort, 2013. "Agreement theorem for neo-additive beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 1-13, January.
    33. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    34. Essid, Samir, 1997. "Choice under risk with certainty and potential effects: A general axiomatic model," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 223-247, October.
    35. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015, January.
    36. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    37. Jean-Philippe Lefort & Adam Dominiak, 2013. "Agreement theorem for neo-additive beliefs," Post-Print hal-01615841, HAL.
    38. J. Ford & D. Kelsey & W. Pang, 2013. "Information and ambiguity: herd and contrarian behaviour in financial markets," Theory and Decision, Springer, vol. 75(1), pages 1-15, July.
    39. Zimper, Alexander, 2012. "Asset pricing in a Lucas fruit-tree economy with the best and worst in mind," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 610-628.
    40. Heath, Chip & Tversky, Amos, 1991. "Preference and Belief: Ambiguity and Competence in Choice under Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 5-28, January.
    41. Adam Dominiak & Jürgen Eichberger & Jean-Philippe Lefort, 2012. "Agreeable trade with pessimism and optimism," Post-Print hal-01615843, HAL.
    42. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    43. Hong, Chew Soo & Wakker, Peter, 1996. "The Comonotonic Sure-Thing Principle," Journal of Risk and Uncertainty, Springer, vol. 12(1), pages 5-27, January.
    44. Wakker, Peter, 1993. "Clarification of some mathematical misunderstandings about Savage's foundations of statistics, 1954," Mathematical Social Sciences, Elsevier, vol. 25(2), pages 199-202, February.
    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. Henderson, Vicky & Hobson, David & Tse, Alex S.L., 2017. "Randomized strategies and prospect theory in a dynamic context," Journal of Economic Theory, Elsevier, vol. 168(C), pages 287-300.
    2. Jinrui Pan & Craig S. Webb & Horst Zank, 2019. "Delayed probabilistic risk attitude: a parametric approach," Theory and Decision, Springer, vol. 87(2), pages 201-232, September.
    3. Katarzyna M. Werner & Horst Zank, 2019. "A revealed reference point for prospect theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 731-773, June.
    4. Meng, Jingyi & Webb, Craig S. & Zank, Horst, 2024. "Mixture independence foundations for expected utility," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    5. Ulrich Schmidt & Horst Zank, 2022. "Chance theory: A separation of riskless and risky utility," Journal of Risk and Uncertainty, Springer, vol. 65(1), pages 1-32, August.
    6. Craig S. Webb, 2017. "Piecewise linear rank-dependent utility," Theory and Decision, Springer, vol. 82(3), pages 403-414, March.

    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. Craig S. Webb, 2017. "Piecewise linear rank-dependent utility," Theory and Decision, Springer, vol. 82(3), pages 403-414, March.
    2. Craig S. Webb, 2017. "Purely subjective variational preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 121-137, June.
    3. 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.
    4. Katarzyna M. Werner & Horst Zank, 2019. "A revealed reference point for prospect theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(4), pages 731-773, June.
    5. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier L'Haridon & Author-Name: Chen Li, 2013. "Learning under ambiguity: An experiment using initial public offerings on a stock market," Economics Working Paper Archive (University of Rennes & University of Caen) 201331, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    6. Alexander Ludwig & Alexander Zimper, 2013. "A decision-theoretic model of asset-price underreaction and overreaction to dividend news," Annals of Finance, Springer, vol. 9(4), pages 625-665, November.
    7. Aurélien Baillon & Han Bleichrodt & Umut Keskin & Olivier l’Haridon & Chen Li, 2018. "The Effect of Learning on Ambiguity Attitudes," Management Science, INFORMS, vol. 64(5), pages 2181-2198, May.
    8. Emy Lécuyer & Jean-Philippe Lefort, 2021. "Put–call parity and generalized neo-additive pricing rules," Theory and Decision, Springer, vol. 90(3), pages 521-542, May.
    9. Dominiak, Adam & Lefort, Jean-Philippe, 2015. "“Agreeing to disagree” type results under ambiguity," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 119-129.
    10. Dean, Mark & Ortoleva, Pietro, 2017. "Allais, Ellsberg, and preferences for hedging," Theoretical Economics, Econometric Society, vol. 12(1), January.
    11. Dominiak, Adam & Lee, Min Suk, 2017. "Coherent Dempster–Shafer equilibrium and ambiguous signals," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 42-54.
    12. Izhakian, Yehuda, 2017. "Expected utility with uncertain probabilities theory," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 91-103.
    13. Nicolas Lampach & Sandrine Spaeter, 2016. "The Efficiency of (strict) Liability Rules revised in Risk and Ambiguity," Working Papers of BETA 2016-29, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    14. Groneck, Max & Ludwig, Alexander & Zimper, Alexander, 2016. "A life-cycle model with ambiguous survival beliefs," Journal of Economic Theory, Elsevier, vol. 162(C), pages 137-180.
    15. Katarzyna Werner & Horst Zank, 2012. "Foundations for Prospect Theory Through Probability Midpoint Consistency," Economics Discussion Paper Series 1210, Economics, The University of Manchester.
    16. Zhihua Li & Julia Müller & Peter P. Wakker & Tong V. Wang, 2018. "The Rich Domain of Ambiguity Explored," Management Science, INFORMS, vol. 64(7), pages 3227-3240, July.
    17. Alexander Zimper, 2011. "Do Bayesians Learn Their Way Out of Ambiguity?," Decision Analysis, INFORMS, vol. 8(4), pages 269-285, December.
    18. Gijs van de Kuilen & Peter P. Wakker, 2011. "The Midweight Method to Measure Attitudes Toward Risk and Ambiguity," Management Science, INFORMS, vol. 57(3), pages 582-598, March.
    19. Mohammed Abdellaoui & Horst Zank, 2022. "Source and Rank-dependent Utility," Post-Print hal-03924295, HAL.
    20. Abdellaoui, Mohammed & Wakker, Peter P., 2020. "Savage for dummies and experts," Journal of Economic Theory, Elsevier, vol. 186(C).

    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:man:sespap:1503. 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: Patrick Macnamara (email available below). General contact details of provider: https://edirc.repec.org/data/semanuk.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.