Rational preferences under ambiguity. (English) Zbl 1277.91018
Summary: This paper analyzes preferences in the presence of ambiguity that are rational in the sense of satisfying the classical ordering condition as well as monotonicity. Under technical conditions that are natural in an Anscombe-Aumann environment, we show that even for such a general preference model, it is possible to identify a set of priors, as first envisioned by D. Ellsberg [Q. J. Econ. 75, No. 4, 643–669 (1961; Zbl 1280.91045)]. We then discuss ambiguity attitudes, as well as unambiguous acts and events, for the class of rational preferences we consider.
Citations:
Zbl 1280.91045References:
| [1] | Amarante M., Filiz E.: Ambiguous events and maxmin expected utility. J Econ Theory 134, 1–33 (2007) · Zbl 1156.91342 · doi:10.1016/j.jet.2005.12.009 |
| [2] | Baillon, A., L’Haridon, O., Placido, L.: Ambiguity models and the Machina paradoxes. Am Econ Rev (forthcoming) |
| [3] | Bewley T.: Knightian decision theory: Part I. Decis Econ Financ 25(2), 79–110 (2002) (first version 1986) · Zbl 1041.91023 · doi:10.1007/s102030200006 |
| [4] | Cerreia-Vioglio, S., Maccheroni, F., Marinacci, M., Montrucchio, L.: Uncertainty Averse Preferences. Carlo Alberto Notebook 77 (2008) · Zbl 1247.91046 |
| [5] | Cerreia-Vioglio, S., Maccheroni, F., Marinacci, M., Montrucchio, L.: Probabilistic Sophistication and Uncertainty Averse Preferences, Università Bocconi, Mimeo (2009) · Zbl 1247.91046 |
| [6] | Ellsberg D.: Risk, ambiguity, and the Savage axioms. Q J Econ 75, 643–669 (1961) · Zbl 1280.91045 · doi:10.2307/1884324 |
| [7] | Epstein L.G.: A definition of uncertainty aversion. Rev Econ Stud 66, 579–608 (1999) · Zbl 0953.91002 · doi:10.1111/1467-937X.00099 |
| [8] | Epstein L.G., Zhang J.: Subjective probabilities on subjectively unambiguous events. Econometrica 69, 265–306 (2001) · Zbl 1020.91048 · doi:10.1111/1468-0262.00193 |
| [9] | Ghirardato P., Marinacci M.: Risk, ambiguity, and the separation of utility and beliefs. Math Oper Res 26(4), 864–890 (2001) · Zbl 1082.91513 · doi:10.1287/moor.26.4.864.10002 |
| [10] | Ghirardato P., Marinacci M.: Ambiguity made precise: a comparative foundation. J Econ Theory 102, 251–289 (2002) · Zbl 1019.91015 · doi:10.1006/jeth.2001.2815 |
| [11] | Ghirardato P., Maccheroni F., Marinacci M.: Differentiating ambiguity and ambiguity attitude. J Econ Theory 118, 133–173 (2004) · Zbl 1112.91021 · doi:10.1016/j.jet.2003.12.004 |
| [12] | Ghirardato P., Maccheroni F., Marinacci M.: Certainty independence and the separation of utility and beliefs. J Econ Theory 120, 129–136 (2005) · Zbl 1080.91506 · doi:10.1016/j.jet.2004.01.002 |
| [13] | Ghirardato, P., Siniscalchi, M.: A More Robust Definition of Multiple Priors. Carlo Alberto Notebook 144 (2010) |
| [14] | Gilboa, I., Marinacci, M.: Ambiguity and the Bayesian Paradigm. Università Bocconi and Tel-Aviv University, Mimeo (2010) · Zbl 1384.03081 |
| [15] | Gilboa I., Maccheroni F., Marinacci M., Schmeidler D.: Objective and subjective rationality in a multiple prior model. Econometrica 78, 755–770 (2010) · Zbl 1229.91103 · doi:10.3982/ECTA8223 |
| [16] | Gilboa I., Schmeidler D.: Maxmin expected utility with a non-unique prior. J Math Econ 18, 141–153 (1989) · Zbl 0675.90012 · doi:10.1016/0304-4068(89)90018-9 |
| [17] | Grant, S., Polak, B.: Generalized Variational Preferences. Rice University and Yale University, Mimeo (2007) |
| [18] | Hurwicz, L.: Optimality Criteria for Decision Making Under Ignorance. Statistics 370, Cowles Commission Discussion Paper (1951) |
| [19] | Klibanoff P., Marinacci M., Mukerji S.: A smooth model of decision making under ambiguity. Econometrica 73, 1849–1892 (2005) · Zbl 1151.91372 · doi:10.1111/j.1468-0262.2005.00640.x |
| [20] | Klibanoff, P., Marinacci, M., Mukerji, S.: Definitions of ambiguous events and the smooth ambiguity model. Econ Theory (2011, this issue). doi: 10.1007/s00199-011-0641-7 · Zbl 1277.91042 |
| [21] | Kopylov I.: Subjective probabilities on ”small” domains. J Econ Theory 133(1), 236–265 (2007) · Zbl 1280.60008 · doi:10.1016/j.jet.2005.11.002 |
| [22] | Kreps D.M.: Notes on the Theory of Choice. Westview Press, Boulder and London (1988) |
| [23] | Maccheroni F., Marinacci M., Rustichini A.: Ambiguity aversion, robustness, and the variational representation of preferences. Econometrica 74, 1447–1498 (2006) · Zbl 1187.91066 · doi:10.1111/j.1468-0262.2006.00716.x |
| [24] | Machina M.J., Schmeidler D.: A more robust definition of subjective probability. Econometrica 60, 745–780 (1992) · Zbl 0763.90012 · doi:10.2307/2951565 |
| [25] | Marinacci M.: Probabilistic sophistication and multiple priors. Econometrica 70, 755–764 (2002) · Zbl 1103.91333 · doi:10.1111/1468-0262.00303 |
| [26] | Nehring K.: Capacities and probabilistic beliefs: a precarious coexistence. Math Soc Sci 38, 197–213 (1999) · Zbl 1073.91571 · doi:10.1016/S0165-4896(97)00017-6 |
| [27] | Nehring, K.: Ambiguity in the Context of Probabilistic Beliefs. UC Davis, Mimeo (2001) |
| [28] | Nehring, K.: Imprecise Probabilistic Beliefs as a Context for Decision-Making Under Ambiguity, UC Davis, Mimeo (2002) · Zbl 1159.91349 |
| [29] | Nehring, K.: Is it Possible to Define Subjective Probabilities in Behavioral Terms? A Comment on Epstein-Zhang (2001), UC Davis, Mimeo (2006) |
| [30] | Nehring, K.: Bernoulli without Bayes: A Theory of Utility-Sophisticated Preferences Under Ambiguity. UC Davis, Mimeo (2007) |
| [31] | Savage L.J.: The Foundations of Statistics. Wiley, New York (1954) · Zbl 0055.12604 |
| [32] | Schmeidler D.: Subjective probability and expected utility without additivity. Econometrica 57, 571–587 (1989) · Zbl 0672.90011 · doi:10.2307/1911053 |
| [33] | Siniscalchi M.: Vector expected utility and attitudes toward variation. Econometrica 77, 801–855 (2009) · Zbl 1182.91061 · doi:10.3982/ECTA7564 |
| [34] | Strzalecki, T.: Probabilistic Sophistication and Variational Preferences. Harvard Institute of Economic Research Discussion Paper Number 2186 (2010) |
| [35] | Zhang J.: Subjective ambiguity, probability and capacity. Econ Theory 20, 159–181 (2002) · Zbl 1032.91050 · doi:10.1007/s001990100207 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
