×

zbMATH — the first resource for mathematics

The \(\alpha \)-MEU model: a comment. (English) Zbl 1247.91061
Summary: P. Ghirardato, F. Maccheroni and M. Marinacci [J. Econ. Theory 118, No. 2, 133–173 (2004; Zbl 1112.91021)] proposed a method for distinguishing between perceived ambiguity and the decision-maker’s reaction to it. They study a general class of preferences which they refer to as invariant biseparable. This class includes CEU and MEU. They axiomatize a subclass of \(\alpha \)-MEU preferences. If attention is restricted to finite state spaces, we show that any \(\alpha \)-MEU preference relation, satisfies GMM’s axioms if and only if \(\alpha =0\) or \(1\), that is, the preferences must be either maxmin or maxmax. We show by example that these axioms may be satisfied when the state space is \([0,1]\).

MSC:
91B16 Utility theory
91B06 Decision theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bauer, H., Probability theory and elements of measure theory, (1972), Holt Rinehart and Winston New York
[2] Bewley, T., Knightian decision theory part I, Decis. econ. finance, 2, 79-110, (2002) · Zbl 1041.91023
[3] Chateauneuf, A.; Eichberger, J.; Grant, S., Choice under uncertainty with the best and worst in mind: NEO-additive capacities, J. econ. theory, 137, 538-567, (2007) · Zbl 1132.91420
[4] Clarke, F.H., Optimization and nonsmooth analysis, (1983), SIAM Publ. Philadelphia · Zbl 0727.90045
[5] Dunford, N.; Schwartz, J.T., Linear operators, (1958), Wiley New York
[6] Eichberger, J.; Grant, S.; Kelsey, D., Differentiating ambiguity: an expository note, Econ. theory, 38, 327-336, (2008) · Zbl 1149.91025
[7] Ghirardato, P.; Macheroni, F.; Marinacci, M., Differentiating ambiguity and ambiguity attitude, J. econ. theory, 118, 133-173, (2004) · Zbl 1112.91021
[8] Gilboa, I.; Schmeidler, D., Maxmin expected utility with a non-unique prior, J. math. econ., 18, 141-153, (1989) · Zbl 0675.90012
[9] Hurwicz, L., Some specification problems and application to econometric models, Econometrica, 19, 343-344, (1951)
[10] Nehring, K., Imprecise probabilistic beliefs as a context of decision-making under ambiguity, J. econ. theory, 144, 1054-1091, (2009) · Zbl 1159.91349
[11] Schmeidler, D., Subjective probability and expected utility without additivity, Econometrica, 57, 571-587, (1989) · Zbl 0672.90011
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.