×

zbMATH — the first resource for mathematics

Choquet rationality. (English) Zbl 1038.91521
Summary: Consider a decision problem under uncertainty for a decision maker with known (utility) payoffs over prizes. The authors call an act Choquet (Shafer, Bernoulli) rational if for some capacity (belief function, probability) over the set of states, it maximizes her “expected” utility. They show that an act may be Choquet rational without being Bernoulli rational, but it is Choquet rational if and only if it is Shafer rational.

MSC:
91B06 Decision theory
91B16 Utility theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bernheim, B.D, Rationalizable strategic behavior, Econometrica, 52, 1007-1028, (1984) · Zbl 0552.90098
[2] Choquet, G, Theory of capacities, Annales de l’institut Fourier (crenoble), 5, 131-295, (1953) · Zbl 0064.35101
[3] Dempster, A.P, Upper and lower probabilities induced by a multi-valued mapping, Ann. math. statist., 38, 325-339, (1967) · Zbl 0168.17501
[4] Ellsberg, D, Risk, ambiguity, and the savage axioms, Quart. J. econom., 75, 643-669, (1961) · Zbl 1280.91045
[5] Epstein, L.G, Preference, rationalizability and equilibrium, J. econ. theory, 73, 1-29, (1997) · Zbl 0886.90193
[6] Ghirardato, P; Le Breton, M, Choquet rationality, Social science working paper 1000, (1996)
[7] Ghirardato, P; Marinacci, M, Ambiguity made precise: A comparative foundation, Social science working paper 1026, (1997)
[8] Gilboa, I; Schmeidler, D, Maxmin expected utility with a non-unique prior, J. math. econ., 18, 141-153, (1989) · Zbl 0675.90012
[9] Klibanoff, P, Characterizing uncertainty aversion through preference for mixtures, CMS-EMS discussion paper 1159, (1996), Northwestern University
[10] Pearce, D.G, Rationalizable strategic behavior and the problem of perfection, Econometrica, 52, 1029-1050, (1984) · Zbl 0552.90097
[11] Rockafellar, R.T, Convex analysis, (1970), Princeton University Press Princeton
[12] Schmeidler, D, Subjective probability and expected utility without additivity, Econometrica, 57, 571-587, (1989) · Zbl 0672.90011
[13] Shafer, G, A mathematical theory of evidence, (1976), Princeton University Press Princeton
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.