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

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  • Sarin, Rakesh
  • Wakker, Peter

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

Article provided by Wiley Blackwell in its journal Review of Economic Studies.

Volume (Year): 64 (1997)
Issue (Month): 3 (July)
Pages: 399-409

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Handle: RePEc:bla:restud:v:64:y:1997:i:3:p:399-409

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  1. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  2. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  3. Frederick Mosteller & Philip Nogee, 1951. "An Experimental Measurement of Utility," Journal of Political Economy, University of Chicago Press, vol. 59, pages 371.
  4. 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.
  5. Maxwell B. Stinchcombe, 1994. "Countably Additive Subjective Probabilities," CARE Working Papers 9403, The University of Texas at Austin, Center for Applied Research in Economics.
  6. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
  7. 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.
  8. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-77, March.
  9. Quiggin, John, 1990. "Stochastic Dominance in Regret Theory," Review of Economic Studies, Wiley Blackwell, vol. 57(3), pages 503-11, July.
  10. Karni, Edi, 1993. "A Definition of Subjective Probabilities with State-Dependent Preferences," Econometrica, Econometric Society, vol. 61(1), pages 187-98, January.
  11. Eichberger, J. & Kelsey, D., 1993. "Uncertainty Aversion and Dynamic Consistency," Discussion Papers 93-08, Department of Economics, University of Birmingham.
  12. Mark J. Machina & David Schmeidler, 1994. "Bayes Without Bernoulli: Simple Conditions for Probabilistically Sophisticated Choice," Discussion Papers 1088, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  14. 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.
  15. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-72, November.
  16. 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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Cited by:
  1. Vincent Feltkamp & Yoram Halevy, 2000. "A Bayesian Approach to Uncertainty Aversion," Econometric Society World Congress 2000 Contributed Papers 1125, Econometric Society.
  2. 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.
  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. 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.

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