Extensions of the subjective expected utility model

Advances in Decision Analysis: From Foundations to Applications

Volumn , Issue , 2007, Pages 253-278

  Nau, Robert F ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67649196209     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511611308.015     Document Type: Chapter

References (112)

1. Allais, M. (1953). Le Comportement de l’Homme Rationnel devant le Risque: Critique des Postulats et Axiomes de l’Ecole Américaine. Econometrica, 21, 503–546.
2. Anscombe, F., and Aumann, R. (1963). A Definition of Subjective Probability. Annals of Mathematical Statistics, 34, 199–205.
3. Arrow, K. (1951). An Extension of the Basic Theorems of Classical Welfare Economics. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press.
4. Arrow, K. (1953/1964). The Role of Securities in the Optimal Allocation of Risk-Bearing. Quarterly Journal of Economics, 31, 91–96.
5. Aumann, R. (1971). Letter to L. J. Savage. Reprinted inDrèze, J. (1987). Essays on Economic Decision Under Uncertainty. London: Cambridge University Press.
6. Bechara, A., Damasio, A., Damasio, H., and Anderson, S. (1994). Insensitivity to Future Consequences Following Damage to Human Prefrontal Cortex. Cognition, 50, 7–15.
7. Bechara, A., Damasio, H., Damasio, A., and Lee, G. (1999). Different Contributions of the Human Amygdala and Ventromedial Prefrontal Cortex to Decision-Making. J. Neuroscience, 19, 473–481.
8. Becker, J., and Sarin, R. (1987). Lottery Dependent Utility. Management Science, 33, 1367–1382.
9. Bell, D. (1982). Regret in Decision Making under Uncertainty. Operations Research, 30, 961–981.
10. Bell. D. (1985). Disappointment in Decision Making under Uncertainty. Operations Research, 33, 1–27.
11. Bernoulli, D. (1738). SpecimenTheoriae Novae de Mensura Sortis. Commentarii Academiae Scientiarum ImperialisPetropolitanae, 5, 175–192. Translation by L.Sommer(1954) Exposition of a New Theory on the Measurement of Risk. Econometrica, 22, 23–36.
12. Bewley, T. (1986). Knightian Decision Theory Part I. Cowles Foundation Discussion Paper No. 807. Reprinted in (2002). Decisions in Economics and Finance, 25, 79–110.
13. Bleichrodt, H., and Pinto, J. (2000). A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis. Management Science, 46, 1485–1496.
14. Bleichrodt, H., Pinto, J., andWakker, P. (2001). Making Descriptive Use of Prospect Theory to Improve the Prescriptive Use of Expected Utility. Management Science, 47, 1498–1514.
15. Camerer, C., Loewenstein, G., and Prelec, D. (2004a). Neuroeconomics: How Neuroscience Can Inform Economics. Journal of Economic Literature, XLIII, 9–64.
16. Camerer, C., Loewenstein, G., and Prelec, D. (2004b). Neuroeconomics: Why Economics Needs Brains. Scandinavian Journal of Economics, 106, 555–579.
17. Chew, S. H. (1983). A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox. Econometrica, 51, 1065–1092.
18. Chew, S.H. and Sagi, J. (2006). Small Worlds: Modeling Attitudes Toward Sources of Uncertainty. Working paper, University of California at Berkeley.
19. Chew, S. H., and Wakker, P. (1996). The Comonotonic Sure-Thing Principle. Journal of Risk and Uncertainty, 12, 5–27.
20. Chew, S.H., Karni, E. and Safra, Z. (1987). Risk Aversion in the Theory of Expected Utility with Rank Dependent Probabilities. Journal of Economic Theory, 42, 370–381.
21. CNRS. (1953). Econometrie, Paris, 12–17 Mai 1952. Colloques Internationaux, 40, Centre National de la Recherche Scientifique, Paris.
22. Damasio, A. (1994). Descartes’ Error: Emotion, Reason, and the Human Brain. New York: Putnam.
23. Damasio, A. (2003). Looking For Spinoza: Joy, Sorrow, and the Feeling Brain. Orlando: Harcourt.
24. de Finetti, B. (1974). Theory of Probability, Vol. 1. New York: Wiley.
25. Debreu, G. (1959). Theory of Value. New Haven: Cowles Foundation.
26. Degroot, M. (1970). Optimal Statistical Decisions. New York: McGraw-Hill.
27. Diecidue, E., andWakker, P. (2001). On the Intuition of Rank-Dependent Utility. Journal of Risk and Uncertainty, 23, 281–298.
28. Dorris, M., and Glimcher, P. (2004) Activity in Posterior Parietal Cortex is Correlated with the Subjective Desirability of an Action. Neuron,44, 365–378.
29. Drèze, J. (1970). Market Allocation Under Uncertainty. European Economic Review, 2, 133–165.
30. Drèze, J. (1987). Essays on Economic Decision Under Uncertainty. London: Cambridge University Press.
31. Eisenberger, R., and Weber, M. (1995). Willingness-to-Pay and Willingness-to-Accept for Risky and Ambiguous Lotteries. Journal of Risk and Uncertainty, 10, 223–233.
32. Ellsberg, D. (1961). Risk, Ambiguity and the Savage Axioms. Quarterly Journal of Economics, 75, 643–669.
33. Ergin, H., and Gul, F. (2004). A Subjective Theory of Compound Lotteries. Working paper, MIT.
34. Fishburn, P. (1970). Utility Theory for Decision Making. New York: Wiley
35. Fishburn, P. (1982). Nontransitive Measurable Utility. Journal of Mathematical Psychology, 26, 31–67.
36. Fishburn, P. and Wakker, P. (1995). The Invention of the Independence Condition for Preferences. Management Science, 41, 1130–1144.
37. Gilboa, I., and Schmeidler, D. (1989). Maxmin Expected Utility with Nonunique Prior. Journal of Mathematical Economics, 18, 141–153.
38. Glimcher, P. (2002). Decisions, Decisions, Decisions: Choosing a Neurobiological Theory of Choice. Neuron, 36, 323–332.
39. Glimcher, P., and Rustichini, A. (2004). Neuroeconomics: The Concilience of Brain and Decision. Science, 306, 447–452.
40. Glimcher, P. (2003). Decisions, Uncertainty, and the Brain: The Science of Neuro Economics. Cambridge, MA and London: MIT Press.
41. Hacking, I. (1967). Slightly More Realistic Personal Probability. Philosophy of Science, 34, 311–325.
42. Hirshleifer, J. (1965). Investment Decision under Uncertainty: Choice-Theoretic Approaches. Quarterly Journal of Economics, 74, 509–536.
43. Hsu, M., Bhatt, M., Adolphs, R., Tranel, D., and Camerer, C. (2005). Neural Systems Responding to Degrees of Uncertainty in Human Decision-Making. Science, 310, 1680–1683.
44. Huettel, S., Stowe, J., Gordon, E., Warner, B., and Platt, M. (2006). Neural Signatures of Economic Preferences for Risk and Ambiguity. Neuron, 49, 765–775.
45. Kadane, J.B., and Winkler, R. L. (1988). Separating Probability Elicitation from Utilities. Journal of the American Statistical Association, 83, 357–363.
46. Kahneman, D. and Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk. Econometrica, 47, 263–291.
47. Karni, E. (1985). Decision-Making under Uncertainty: The Case of State-Dependent Preferences. Cambridge, MA: Harvard University Press.
48. Karni, E. (1996). Probabilities and Beliefs. Journal of Risk and Uncertainty, 13, 249–262.
49. Karni, E. and Mongin, P. (2000) On the Determination of Subjective Probabilities by Choices. Management Science, 46, 233–248.
50. Karni, E., Schmeidler, D., and Vind, K. (1983). On State Dependent Preferences and Subjective Probabilities. Econometrica, 51, 1021–1031.
51. Karni, E., and Schmeidler, D. (1993). On the Uniqueness of Subjective Probabilities. Economic Theory, 3, 267–277.
52. Klibanoff, P., Marinacci, M., and Mukerji, S. (2005). A Smooth Model of Decision Making Under Ambiguity. Econometrica, 73, 1849–1892.
53. Knight, F. (1921). Risk, Uncertainty, and Profit. New York: Houghton Mifflin.
54. Koopman, B. (1940). Axioms and Algebra of Intuitive Probability. Annals of Mathematics, 41, 269–292.
55. Kreps, D. (1988). Notes on the Theory of Choice. Boulder: Westview Press.
56. Kyburg, H. (1974). The Logical Foundations of Statistical Inference. Dordrecht: Reidel.
57. Levi, I. (1980). The Enterprise of Knowledge. Cambridge, MA: MIT Press.
58. Loomes, G., and Sugden, R. (1982). Regret Theory: An Alternative Theory of Rational Choice under Uncertainty. Economic Journal, 92, 805–824.
59. Luce, R.D. (2000). Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches. Mahwah, NJ: Erlbaum.
60. Luce, R. D., and Fishburn, P. (1991). Rank-and Sign-Dependent Linear Utility Models for Finite First-Order Gambles. Journal of Risk and Uncertainty, 4, 29–59.
61. Luce, R.D., and Narens, L. (1985). Classification of Concatenation Measurement Structures According to Scale Type. Journal of Mathematical Psychology, 29, 1–72.
62. Luce, R. D., and Manders, K. (1988). Rank-Dependent Subjective Expected-Utility Representations. Journal of Risk and Uncertainty, 1, 305–332.
63. Machina, M. (1982). Expected Utility without the Independence Axiom. Econometrica, 50, 227–323.
64. Machina, M. (2005). ‘Expected Utility/Subjective Probability’ Analysis without the Sure-Thing Principle or Probabilistic Sophistication. Economic Theory, 26, 1–62.
65. Machina, M. and Schmeidler, D. (1992). A More Robust Definition of Subjective Probability. Econometrica, 60, 745–780.
66. Moskowitz, H., Preckel, P. and Yang, A. (1993). Decision Analysis with Incomplete Utility and Probability Information. Operations Research, 41, 864–879.
67. Nau, R. (1989). Decision Analysis with Indeterminate or Incoherent Probabilities. Annals of Operations Research, 19, 375–403.
68. Nau, R. (1992). Indeterminate Probabilities on Finite Sets. Annals of Statistics, 20, 1737–1767.
69. Nau, R. (1995). Coherent Decision Analysis with Inseparable Probabilities and Utilities. Journal of Risk and Uncertainty, 10, 71–91.
70. Nau, R. (2001a). De Finetti Was Right: Probability Does Not Exist. Theory and Decision, 59, 89–124.
71. Nau, R. (2001b). Uncertainty Aversion with Second-Order Probabilities and Utilities. Proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications. Web site: http: //www.sipta.org/isipta01/proceedings/063.html
72. Nau, R. (2003). A Generalization of Pratt-Arrow Measure to Non-Expected-Utility Preferences and Inseparable Probability and Utility. Management Science, 49, 1089–1104.
73. Nau, R. (2006a). Uncertainty Aversion with Second-Order Utilities and Probabilities. Management Science, 52, 136–145.
74. Nau, R. (2006b). The Shape of Incomplete Preferences. Annals of Statistics34, 5, 155–164.
75. Nau, R. and McCardle, K. (1991). Arbitrage, Rationality, and Equilibrium. Theory and Decision, 31, 199–240.
76. Pinker, S. (1997). How the Mind Works. New York: Norton.
77. Pinker, S. (2002). The Blank Slate: the Modern Denial of Human Nature. New York: Viking.
78. Platt, M. and Glimcher, P. (1999). Neural Correlates of Decision Variables in Parietal Cortex. Nature400, 233–238.
79. Prelec, D. (1998). The Probability Weighting Function. Econometrica, 66, 497–527.
80. Prelec, D., and Loewenstein, G. (1998). The Red and the Black: Mental Accounting of Savings and Debt. Marketing Science, 17, 4–28.
81. Quiggin, J. (1982). A Theory of Anticipated Utility. Journal of Economic Behaviour and Organization, 3, 323–343.
82. Rios Insua, D. (1990). Sensitivity Analysis in Multiobjective Decision Making. Berlin: Springer-Verlag.
83. Rios Insua, D. (1992). On the Foundations of Decision Making Under Partial Information. Theory and Decision, 33, 83–100.
84. Rios Insua, D., and Ruggeri, F. (2000). Robust Decision Analysis. New York: Springer-Verlag.
85. Rubin, H. (1987). A Weak System of Axioms for “Rational” Behavior and the Non-Separability of Utility from Prior. Statistics and Decisions, 5, 47–58.
86. Rubinstein, M. (1976). The Strong Case for the Generalized Logarithmic Utility Model as the Premier Model of Financial Markets. Journal of Finance, 31, 551–571.
87. Savage, L. (1954). The Foundations of Statistics. New York: Wiley.
88. Schervish, M., Seidenfeld, T., and Kadane, J. (1990). State-Dependent Utilities. Journal of the American Statistical Association, 85, 840–847.
89. Schmeidler, D. (1989). Subjective Probability and Expected Utility without Additivity. Econometrica, 57, 571–587.
90. Schmidt, U. (2004). Alternatives to Expected Utility: Formal Theories. In S. Barberà, P. Hammond, and C. Seidl, Handbook of Utility Theory, Vol. 2. Dordrecht: Kluwer.
91. Segal, U. (1989). Anticipated Utility: A Measure Representation Approach. Annals of Operations Research, 19, 359–373.
92. Shafer, G. (1986). Savage Revisited (including comments). Statistical Science, 1, 463–501.
93. Shiv, B., Loewenstein, G., Bechara, A., Damasio, H., and Damasio, A. (2005). Investment Behavior and the Negative Side of Emotion. Psychological Science, 16, 435–439.
94. Smith, C. (1961). Consistency in Statistical Inference and Decision. Journal of the Royal Statistical Society B, 23, 1–25.
95. Smith, J., and Nau, R. (1995). Valuing Risky Projects: Option Pricing Theory and Decision Analysis. Management Science, 41, 795–816.
96. Starmer, C. (2000). Developments in Non-Expected UtilityTheory: The Hunt for a Descriptive Theory of Choice under Risk. Journal of Economic Literature, XXXVIII, 332–82.
97. Stigler, G. (1950). The Development of Utility Theory: I; II. Journal of Political Economy, 58, 307–327; 373–396.
98. Sugden, R. (2004). Alternatives to Expected Utility: Foundations. In S. Barberà, P. Hammond, and C. Seidl, Handbook of Utility Theory, Vol. 2. Dordrecht: Kluwer.
99. Tversky, A., and Fox, C. (1995). Weighing Risk and Uncertainty. Psychological Review, 102, 269–283.
100. Tversky, A., and Kahneman, D. (1992). Advances in Prospect Theory: Cumulative Representation of Uncertainty. Journal of Risk and Uncertainty, 5, 297–323.
101. van de Kuilen, G., and Wakker, P. (2006). Learning in the Allais Paradox. Journal of Risk and Uncertainty, 33, 155–164.
102. von Neumann, J., and Morgenstern, O. (1947). Theory of Games and Economic Behavior. Princeton: Princeton University Press.
103. Wakker, P. (1989). Additive Representations of Preferences: A New Foundation for Decision Analysis. Dordrecht: Kluwer.
104. Wakker, P. (1991). Additive Representations on Rank-Ordered Sets. I. The Algebraic Approach. Journal of Mathematical Psychology, 35, 501–531.
105. Wakker, P. (1996) The Sure-Thing Principle and the Comonotonic Sure-Thing Principle: An Axiomatic Analysis. Journal of Mathematical Economics, 25, 213–227.
106. Wakker, P. (2006). Annotated References on Decisions and Uncertainty. Web site: http://www1.fee.uva.nl/creed/wakker/refs/rfrncs.htm. Accessed 11/14/06.
107. Wakker, P., and Tversky, A. (1993). An Axiomatization of Cumulative Prospect Theory. Journal of Risk and Uncertainty, 7, 147–176.
108. Wakker, P., and Zank, H. (1999). State Dependent Expected Utility for Savage’s State Space. Mathematics of Operations Research, 24, 8–34.
109. Walley, P. (1991). Statistical Reasoning with Imprecise Probabilities. London: Chapman & Hall.
110. Wu, G., and Gonzalez, R. (1996). Curvature of the Probability Weighting Function. Management Science, 42, 1676–1690.
111. Yaari, M. (1969). Some Remarks on Measures of Risk Aversion and Their Uses. Journal of Economic Theory, 1, 315–329.
112. Yaari, M. (1987). The Dual Theory of Choice under Risk. Econometrica, 55, 95–115.