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Choice under Uncertainty with the Best and Worst in Mind: Neo-additive Capacities

  • Chateauneuf, Alain

    ()

    (CERMSEM Université Paris I)

  • Eichberger, Jürgen

    ()

    (Sonderforschungsbereich 504)

  • Grant, Simon

    ()

    (Department of Economics Rice University)

The concept of a non-extreme-outcome-additive capacity (neo-additive capacity ) is introduced. Neo-additive capacities model optimistic and pessimistic attitudes towards uncer-tainty as observed in many experimental studies. Moreover, neo-additive capacities can be applied easily in economic problems, as we demonstrate by examples. This paper provides an axiomatisation of Choquet expected utility with neo-capacities in a framework of purely subjective uncertainty.

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Paper provided by Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim in its series Sonderforschungsbereich 504 Publications with number 03-10.

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Length: 44 pages
Date of creation: 03 Jun 2003
Date of revision:
Handle: RePEc:xrs:sfbmaa:03-10
Note: We would like to thank Michele Cohen, Peter Hartley, Jean-Yves Jaffray, Mark Machina, Klaus Nehring, Matthew Ryan, Jean-Marc Tallon, and Jean-Christophe Vergnaud for extremely stimulating and helpful discussions. Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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  1. Hong Chew Soo & Karni Edi, 1994. "Choquet Expected Utility with a Finite State Space: Commutativity and Act-Independence," Journal of Economic Theory, Elsevier, vol. 62(2), pages 469-479, April.
  2. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo & Siniscalchi, Marciano, 2001. "A Subjective Spin on Roulette Wheels," Working Papers 1127, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. Mehra, Rajnish & Prescott, Edward C., 1985. "The equity premium: A puzzle," Journal of Monetary Economics, Elsevier, vol. 15(2), pages 145-161, March.
  4. Jürgen Eichberger & David Kelsey, 1999. "E-Capacities and the Ellsberg Paradox," Theory and Decision, Springer, vol. 46(2), pages 107-138, April.
  5. 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 1039-59, July.
  6. Nakamura, Yutaka, 1990. "Subjective expected utility with non-additive probabilities on finite state spaces," Journal of Economic Theory, Elsevier, vol. 51(2), pages 346-366, August.
  7. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July.
  8. Ghirardato, Paolo & Marinacci, Massimo, 2000. "Risk, Ambigity and the Separation of Utility and Beliefs," Working Papers 1085, California Institute of Technology, Division of the Humanities and Social Sciences.
  9. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
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  13. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
  14. Kilka, Michael & Weber, Martin, 1998. "What Determines the Shape of the Probability Weighting Function under Uncertainty?," Sonderforschungsbereich 504 Publications 98-11, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  15. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  16. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
  17. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  18. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279.
  19. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 579-608, July.
  20. Ramsey, Frank P., 1926. "Truth and Probability," Histoy of Economic Thought Chapters, in: Braithwaite, R. B. (ed.), The Foundations of Mathematics and other Logical Essays, chapter 7, pages 156-198 McMaster University Archive for the History of Economic Thought.
  21. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
  22. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-80, November.
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