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Decomposable Choice under Uncertainty

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

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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  2. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-92, July.
  3. Epstein, Larry G., 1986. "Implicitly additive utility and the nature of optimal economic growth," Journal of Mathematical Economics, Elsevier, vol. 15(2), pages 111-128, April.
  4. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
  5. Vind, Karl, 1991. "Independent preferences," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 119-135.
  6. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November.
  7. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
  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 J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-80, July.
  10. 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.
  11. Peter A. Diamond, 1967. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparison of Utility: Comment," Journal of Political Economy, University of Chicago Press, vol. 75, pages 765.
  12. Fishburn, Peter C., 1990. "Continuous nontransitive additive conjoint measurement," Mathematical Social Sciences, Elsevier, vol. 20(2), pages 165-193, October.
  13. Segal, Uzi, 1992. "Additively separable representations on non-convex sets," Journal of Economic Theory, Elsevier, vol. 56(1), pages 89-99, February.
  14. Edward SchleeE, 1997. "The sure thing principle and the value of information," Theory and Decision, Springer, vol. 42(1), pages 21-36, January.
  15. Hong Chew Soo & Epstein Larry G. & Wakker Peter, 1993. "A Unifying Approach to Axiomatic Non-expected Utility Theories: Correction and Comment," Journal of Economic Theory, Elsevier, vol. 59(1), pages 183-188, February.
  16. Costis Skiadas, 1997. "Conditioning and Aggregation of Preferences," Econometrica, Econometric Society, vol. 65(2), pages 347-368, March.
  17. Gul, Faruk & Lantto, Outi, 1990. "Betweenness satisfying preferences and dynamic choice," Journal of Economic Theory, Elsevier, vol. 52(1), pages 162-177, October.
  18. Chew, S. H. & Epstein, L. G., 1989. "A unifying approach to axiomatic non-expected utility theories," Journal of Economic Theory, Elsevier, vol. 49(2), pages 207-240, December.
  19. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-86, May.
  20. Skiadas, Costis, 1997. "Subjective Probability under Additive Aggregation of Conditional Preferences," Journal of Economic Theory, Elsevier, vol. 76(2), pages 242-271, October.
  21. Epstein Larry G. & Le Breton Michel, 1993. "Dynamically Consistent Beliefs Must Be Bayesian," Journal of Economic Theory, Elsevier, vol. 61(1), pages 1-22, October.
  22. Johnsen, Thore H & Donaldson, John B, 1985. "The Structure of Intertemporal Preferences under Uncertainty and Time Consistent Plans," Econometrica, Econometric Society, vol. 53(6), pages 1451-58, November.
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