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Piecewise Additivity for Nonexpected Utility

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  • 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
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Suggested Citation

  • Craig S. Webb, 2015. "Piecewise Additivity for Nonexpected Utility," The School of Economics Discussion Paper Series 1503, Economics, The University of Manchester.
  • Handle: RePEc:man:sespap:1503
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    File URL: http://hummedia.manchester.ac.uk/schools/soss/economics/discussionpapers/EDP-1503.pdf
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Itzhak Gilboa, 1988. "A Combination of Expected Utility and Maxmin Decision Criteria," Post-Print hal-00753244, HAL.
    4. 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.
    5. Aylit Tina Romm, 2014. "An interpretation of focal point responses as non-additive beliefs," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 9(5), pages 387-402, September.
    6. 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.
    7. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015, June.
    8. Schmidt, Ulrich & Zimper, Alexander, 2003. "Security and potential level preferences with thresholds," Papers 03-29, Sonderforschungsbreich 504.
    9. Eichberger, Jürgen & Grant, Simon & Lefort, Jean-Philippe, 2008. "Neo-additive capacities and updating," Papers 08-31, Sonderforschungsbreich 504.
    10. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
    11. 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.
    12. repec:dau:papers:123456789/7604 is not listed on IDEAS
    13. Dominiak, Adam & Eichberger, Jürgen & Lefort, Jean-Philippe, 2012. "Agreeable trade with optimism and pessimism," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 119-126.
    14. 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.
    15. 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.
    16. 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.
    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. Jürgen Eichberger & Simon Grant & Jean-Philippe Lefort, 2012. "Generalized neo-additive capacities and updating," Post-Print hal-01615858, HAL.
    19. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
    20. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    21. Craig R. Fox & Amos Tversky, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 585-603.
    22. J L Ford, David Kelsey and W Pang, 2005. "Ambiguity in Financial Markets: Herding and Contrarian Behaviour," Discussion Papers 05-11, Department of Economics, University of Birmingham.
    23. repec:dau:papers:123456789/7332 is not listed on IDEAS
    24. 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.
    25. 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.
    26. 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.
    27. 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.
    28. 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.
    29. 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.
    30. Wakker, Peter, 1989. "Continuous subjective expected utility with non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 1-27, February.
    31. 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.
    32. 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.
    33. Adam Dominiak & Jürgen Eichberger & Jean-Philippe Lefort, 2012. "Agreeable trade with pessimism and optimism," Post-Print hal-01615843, HAL.
    34. Mohammed Abdellaoui & Peter Wakker, 2005. "The Likelihood Method for Decision under Uncertainty," Theory and Decision, Springer, vol. 58(1), pages 3-76, February.
    35. 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.
    36. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    37. 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.
    38. 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.
    39. 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.
    40. Mohammed Abdellaoui & Laetitia Placido & Aurélien Baillon & P.P. Wakker, 2011. "The Rich Domain of Uncertainty: Source Functions and Their Experimental Implementation," Post-Print hal-00609214, HAL.
    41. repec:dau:papers:123456789/8588 is not listed on IDEAS
    42. repec:hal:journl:halshs-00177057 is not listed on IDEAS
    43. 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.
    44. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, Oxford University Press, vol. 75(4), pages 643-669.
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    1. repec:kap:theord:v:82:y:2017:i:3:d:10.1007_s11238-016-9569-5 is not listed on IDEAS
    2. 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.

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    JEL classification:

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

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