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Decomposable Choice under Uncertainty

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  • Grant, Simon
  • Kajii, Atsushi
  • Polak, Ben

Abstract

Savage motivated his Sure Thing Principle by arguing that, whenever an act would be preferred if an event obtains and preferred if that event did not obtain, then it should be preferred overall. The idea that it should be possible to decompose and recompose decision problems in this way has normative appeal. We show, however, that it does not require the full separability across events implicit in Savage's axiom. We formulate a weaker axiom that suffices for decomposability, and show that this implies an implicit additive representation. Our decomposability property makes local necessary conditions for optimality, globally sufficient. Thus, it is useful in computing optimal acts. It also enables Nash behavior in games of incomplete information to be decentralized to the agent-normal form. None of these results rely on probabilistic sophistication; indeed, our axiom is consistent with the Ellsberg paradox. If we assume probabilistic sophistication, however, then the axiom holds if and only if the agent's induced preferences over lotteries satisfy betweenness.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 92 (2000)
Issue (Month): 2 (June)
Pages: 169-197

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Handle: RePEc:eee:jetheo:v:92:y:2000:i:2:p:169-197

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Web page: http://www.elsevier.com/locate/inca/622869

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  1. Skiadas, Costis, 1997. "Subjective Probability under Additive Aggregation of Conditional Preferences," Journal of Economic Theory, Elsevier, vol. 76(2), pages 242-271, October.
  2. Costis Skiadas, 1997. "Conditioning and Aggregation of Preferences," Econometrica, Econometric Society, vol. 65(2), pages 347-368, March.
  3. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-86, May.
  4. Vind, Karl, 1991. "Independent preferences," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 119-135.
  5. Grant, Simon, 1995. "Subjective Probability without Monotonicity: Or How Machina's Mom May Also Be Probabilistically Sophisticated," Econometrica, Econometric Society, vol. 63(1), pages 159-89, January.
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  7. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November.
  8. Grant, Simon & Kajii, Atsushi & Polak, Ben, 1992. "Many good choice Axioms: When can many-good lotteries be treated as money lotteries?," Journal of Economic Theory, Elsevier, vol. 56(2), pages 313-337, April.
  9. Machina,Mark & Schmeidler,David, 1991. "A more robust definition of subjective probability," Discussion Paper Serie A 365, University of Bonn, Germany.
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  13. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
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Citations

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Cited by:
  1. Atsushi Kajii & Takashi Ui, 2004. "Trade with Heterogeneous Multiple Priors," KIER Working Papers 582, Kyoto University, Institute of Economic Research.
  2. Halevy, Yoram, 2004. "The possibility of speculative trade between dynamically consistent agents," Games and Economic Behavior, Elsevier, vol. 46(1), pages 189-198, January.
  3. Simon Grant & Atsushi Kajii & Ben Polak, 1998. "On the Skiadas 'Conditional Preference Approach' to Choice Under Uncertainty," Cowles Foundation Discussion Papers 1178, Cowles Foundation for Research in Economics, Yale University.
  4. Atsushi Kajii & Takashi Ui, 2007. "Interim Efficient Allocations under Uncertainty," KIER Working Papers 642, Kyoto University, Institute of Economic Research.
  5. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2013. "Savage Games: A Theory of Strategic Interaction with Purely Subjective Uncertainty," Risk and Sustainable Management Group Working Papers 151501, University of Queensland, School of Economics.
  6. Ozaki, Hiroyuki, 2009. "Conditional implicit mean and the law of iterated integrals," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 1-15, January.

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