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A single-stage approach to Anscombe and Aumann's expected utility

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Author Info
Sarin, R.
Wakker, P. (Tilburg University, Center for Economic Research)

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Abstract

Anscombe and Aumann showed that if one accepts the existence of a physical randomizing device such as a roulette wheel then Savage's derivation of subjective expected utility can be considerably simplified. They, however, invoked compound gambles to define their axioms. We demonstrate that the subjective expected utility derivation can be further simplified and need not invoke compound gambles. Our simplification is obtained by closely following the steps by which probabilities and utilities are revealed.

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

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

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Find related papers by JEL classification:
D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. 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. [Downloadable!] (restricted)
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  2. Eichberger, J. & Kelsey, D., 1993. "Uncertainty Aversion and Dynamic Consistency," Discussion Papers 93-08, Department of Economics, University of Birmingham.
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  3. Green, Edward J & Osband, Kent, 1991. "A Revealed Preference Theory for Expected Utility," Review of Economic Studies, Blackwell Publishing, vol. 58(4), pages 677-96, July. [Downloadable!] (restricted)
  4. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-72, November. [Downloadable!] (restricted)
  5. Quiggin, John, 1990. "Stochastic Dominance in Regret Theory," Review of Economic Studies, Blackwell Publishing, vol. 57(3), pages 503-11, July. [Downloadable!] (restricted)
  6. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July. [Downloadable!] (restricted)
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  7. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February. [Downloadable!] (restricted)
  8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May. [Downloadable!] (restricted)
  9. Loomes, Graham & Sugden, Robert, 1986. "Disappointment and Dynamic Consistency in Choice under Uncertainty," Review of Economic Studies, Blackwell Publishing, vol. 53(2), pages 271-82, April. [Downloadable!] (restricted)
  10. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-98, January. [Downloadable!] (restricted)
  11. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-77, March. [Downloadable!] (restricted)
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  1. 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. [Downloadable!]
  2. Halevy, Yoram & Ozdenoren, Emre, 2008. "Uncertainty and Compound Lotteries: Calibration," Micro Theory Working Papers yoram_halevy-2008-7, Microeconomics.ca Website, revised 17 Jun 2008. [Downloadable!]
  3. Mark J. Machina, 2001. "Almost-Objective Uncertainty," University of California at San Diego, Economics Working Paper Series 2001-12, Department of Economics, UC San Diego. [Downloadable!]
  4. Vincent Feltkamp & Yoram Halevy, 1999. "- A Bayesian Approach To Uncertainty Aversion," Working Papers. Serie AD 1999-14, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
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