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A Single-Stage Approach to Anscombe and Aumann's Expected Utility

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  • Sarin, R.
  • Wakker, P.P.

    (Tilburg University, Center for Economic Research)

Abstract

F. J. Anscombe and R. J. Aumann (1963) showed that, if one accepts the existence of a physical randomizing device such as a roulette wheel, then L. J. Savage's derivation of subjective expected utility can be considerably simplified. They, however, invoked compound gambles to define their axioms. The authors demonstrate that the subjective expected utility derivation can be further simplified and need not invoke compound gambles. Their simplification is obtained by closely following the steps by which probabilities and utilities are elicited. Copyright 1997 by The Review of Economic Studies Limited.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 1996-45.

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Date of creation: 1996
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Handle: RePEc:dgr:kubcen:199645

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Related research

Keywords: expected utility theory; decision analysis; revealed preference;

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  1. Uzi Segal, 2000. "Two Stage Lotteries Without the Reduction Axiom," Levine's Working Paper Archive 7599, David K. Levine.
  2. Loomes, Graham & Sugden, Robert, 1986. "Disappointment and Dynamic Consistency in Choice under Uncertainty," Review of Economic Studies, Wiley Blackwell, vol. 53(2), pages 271-82, April.
  3. Machina Mark J. & Schmeidler David, 1995. "Bayes without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice," Journal of Economic Theory, Elsevier, vol. 67(1), pages 106-128, October.
  4. Stinchcombe, Maxwell B, 1997. "Countably Additive Subjective Probabilities," Review of Economic Studies, Wiley Blackwell, vol. 64(1), pages 125-46, January.
  5. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July.
  6. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-72, November.
  7. Quiggin, John, 1990. "Stochastic Dominance in Regret Theory," Review of Economic Studies, Wiley Blackwell, vol. 57(3), pages 503-11, July.
  8. R. Duncan Luce & Detlof von Winterfeldt, 1994. "What Common Ground Exists for Descriptive, Prescriptive, and Normative Utility Theories?," Management Science, INFORMS, vol. 40(2), pages 263-279, February.
  9. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  10. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  11. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-98, January.
  12. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  13. Green, Edward J & Osband, Kent, 1991. "A Revealed Preference Theory for Expected Utility," Review of Economic Studies, Wiley Blackwell, vol. 58(4), pages 677-96, July.
  14. Eichberger, Jurgen & Kelsey, David, 1996. "Uncertainty Aversion and Dynamic Consistency," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(3), pages 625-40, August.
  15. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  16. Frederick Mosteller & Philip Nogee, 1951. "An Experimental Measurement of Utility," Journal of Political Economy, University of Chicago Press, vol. 59, pages 371.
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Cited by:
  1. Feltkamp, Vincent & Halevy, Yoram, 2004. "A Bayesian Approach to Uncertainty Aversion," Microeconomics.ca working papers halevy-04-02-13-07-48-37, Vancouver School of Economics, revised 25 Feb 2014.
  2. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2013. "Mixed Extensions of Decision Problems under Uncertainty," Working Papers 485, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  3. Machina, Mark J, 2001. "Almost-Objective Uncertainty," University of California at San Diego, Economics Working Paper Series qt3ps1k85f, Department of Economics, UC San Diego.
  4. Francis C. Chu & Joseph Y. Halpern, 2004. "Great expectations. Part II: Generalized expected utility as a universal decision rule," Game Theory and Information 0411004, EconWPA.

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