Decision theory under ambiguity

Journal of Economic Surveys

Volumn 26, Issue 2, 2012, Pages 234-270

  Etner, Johanna ^a   Jeleva, Meglena ^b   Tallon, Jean Marc ^c  

^a Centre universitaire des Saints Pères   (France)

^b UNIVERSITÉ DU MAINE   (France)

^c UNIVERSITÉ PARIS 1 PANTHÉON SORBONNE   (France)

Author keywords

Ambiguity; Ambiguity aversion; Decision; Uncertainty

Indexed keywords

BAYESIAN ANALYSIS; DECISION MAKING; ECONOMIC THEORY; MODELING; THEORETICAL STUDY; UNCERTAINTY ANALYSIS;

EID: 84856758066     PISSN: 09500804     EISSN: 14676419     Source Type: Journal    
DOI: 10.1111/j.1467-6419.2010.00641.x     Document Type: Review

References (154)

1. Abdellaoui, M., Baillon, A., Placido, L. and Wakker, P. (2009) The rich domain of uncertainty. Discussion Paper, Erasmus School of Economics, Erasmus University, forthcoming American Economic Review.
2. Ahn, D., Choi, S., Gale, D. and Kariv, S. (2009) Estimating ambiguity aversion in a portfolio choice experiment. Working Paper.
3. Akay, A., Martinsson, P., Medhin, H. and Trautmann, S. (2009) Attitudes toward uncertainty among the poor: evidence from rural ethiopia. Discussion Paper 4225, IZA.
4. Al Najjar, N. and Weinstein, J. (2009) The ambiguity aversion literature: a critical assessment. Economics and Philosophy 25: 249-284.
5. Allais, M. (1953) Le comportement de l'homme rationnel devant le risque: critique des postulats de l'école américaine. Econometrica 21: 503-546.
6. Amarante, M. (2009) Foundations of neo-Bayesian statistics. Journal of Economic Theory 144: 2146-2173.
7. Amarante, M. and Filiz, E. (2007) Ambiguous events and maxmin expected utility. Journal of Economic Theory 134: 1-33.
8. Andersen, S., Fountain, J., Harrison, G. and Rutstrom, E. (2009) Estimating aversion to uncertainty. Mimeo.
9. Anscombe, F. and Aumann, R. (1963) A definition of subjective probability. Annals of Mathematical Statistics 34: 199-205.
10. Arrow, K. and Hurwicz, L. (1972) An optimality criterion for decision making under ignorance. In C. Carter and J. Ford (eds), Uncertainty and Expectations in Economics (pp. 1-11). Oxford: B. Blackwell.
11. Asano, T. (2006) Portfolio inertia under ambiguity. Mathematical Social Sciences 52: 223-232.
12. Bewley, T. (1986) Knightian decision theory: Part I. Discussion Paper 807, Cowles Foundation.
13. Billot, A., Chateauneuf, A., Gilboa, I. and Tallon, J.-M. (2000) Sharing beliefs: between agreeing and disagreeing. Econometrica 68(3): 685-694.
14. Borghans, L., Golsteyn, B., Heckman, J. and Meijers, H. (2009) Gender differences in risk aversion and ambiguity aversion. Discussion Paper 3985, IZA.
15. Bossaerts, P., Ghirardato, P., Guarnaschelli, S. and Zame, W. (2010) Ambiguity in asset markets: theory and experiment. Review of Financial Studies, 23: 1325-1359.
16. Burks, S., Carpenter, J., Gotte, L. and Rustichini, A. (2008) Cognitive skills explain economic prefrences, strategic behavior, and job attachment. Discussion Paper 3609, IZA.
17. Cabantous, L. (2007) Ambiguity aversion in the field of insurance: insurer's attitude to imprecise and conflicting probability estimates. Theory and Decision 62: 219-240.
18. Camerer, C. and Kunreuther, H. (1989) The effects of financial incentives in experiments: a review of capital-labor-production framework. Journal of Risk and Uncertainty 19: 7-42.
19. Camerer, C. and Weber, M. (1992) Recent developments in modeling preferences: uncertainty and ambiguity. Journal of Risk and Uncertainty 5: 325-370.
20. Cao, H., Wang, T. and Zhang, H. (2005) Model uncertainty, limited market participation, and asset prices. Review of Financial Studies 18: 1219-1251.
21. Chakravarty, S. and Roy, J. (2009) Recursive expected utility and the separation of attitudes towards risk and ambiguity: an experimental study. Theory and Decision 66(3): 199-228.
22. Chateauneuf, A. (1994) Modeling attitudes towards uncertainty and risk through the use of Choquet integral. Annals of Operations Research 52: 3-20.
23. Chateauneuf, A. and Faro, J. (2009) Ambiguity through confidence functions. Journal of Mathematical Economics, 45(9-10): 535-558.
24. Chateauneuf, A. and Tallon, J.-M. (2002) Diversification, convex preferences and non-empty core in the Choquet expected utility model. Economic Theory 19(3): 509-523.
25. Chateauneuf, A., Dana, R.-A. and Tallon, J.-M. (2000) Optimal risk-sharing rules and equilibria with Choquet expected utility. Journal of Mathematical Economics 34: 191-214.
26. Chateauneuf, A., Cohen, M. and Meilijson, I. (2004) Four notions of mean-preserving increase in risk, risk attitudes and applications to the Rank-dependent expected utility model. Journal of Mathematical Economics 40: 547-571.
27. Chateauneuf, A., Eichberger, J. and Grant, S. (2007) Choice under uncertainty with the best and worst in mind: neo-additive capacities. Journal of Economic Theory 137: 538-567.
28. Chen, Z. and Epstein, L. (2002) Ambiguity, risk, and asset returns in continuous time. Econometrica 70: 1403-1443.
29. Chew, S. and Sagi, J. (2006) Event exchangeability: small worlds probabilistic sophistication without continuity or monotonicity. Econometrica 74: 771-786.
30. Chew, S. and Sagi, J. (2008) Small worlds: modeling attitudes toward sources of uncertainty. Journal of Economic Theory 139: 1-24.
31. Chow, C. and Sarin, R. (2002) Known, unknown and unknowable uncertainties. Theory and Decision 52: 127-138.
32. Cohen, M. (1995) Risk-aversion concepts in expected- and non-expected-utility models. The Geneva Papers on Risk and Insurance Theory 20: 73-91.
33. Cohen, M. and Jaffray, J.-Y. (1980) Rational behavior under complete ignorance. Econometrica 48(5): 1281-1299.
34. Cohen, M., Jaffray, J.-Y. and Said, T. (1985) Individual behavior under risk and under uncertainty: an experimental study. Theory and Decision 18: 203-228.
35. Cohen, M., Jaffray, J.-Y. and Said, T. (1987) Experimental comparison of individual behavior under risk and under uncertainty for gains and for losses. Organizational Behavior and Human Decision Processes 39: 1-22.
36. Cohen, M., Tallon, J.-M. and Vergnaud, J.-C. (2009) An experimental investigation of imprecision attitude and its relation with risk attitude and impatience. Mimeo, Université Paris I.
37. Condie, S. (2008) Living with ambiguity: prices and survival when investors have heterogeneous preferences for ambiguity. Economic Theory 36: 81-108.
38. Curley, S. and Yates, F. (1985) The center and range of the probability interval as factors affecting ambiguity preferences. Organizational Behavior and Human Decision Processes 36: 272-287.
39. Dana, R. (2004) Ambiguity, uncertainty aversion and equilibrium welfare. Economic Theory 23: 569-587.
40. Dekel, E., Lipman, B. and Rustichini, A. (2001) Representing preferences with a unique subjective state space. Econometrica 69: 891-934.
41. Di Mauro, C. and Maffioletti, A. (2004) Attitudes to risk and attitudes to uncertainty: experimental evidence. Applied Economics 36: 357-372.
42. Dominiak, A., Dürschz, P., and Lefort, J.-P. (2009) A dynamic Ellsberg urn experiment. Discussion Paper Series 487, University of Heidelberg.
43. Dow, J. and Werlang, S. (1992) Uncertainty aversion, risk aversion, and the optimal choice of portfolio. Econometrica 60(1): 197-204.
44. Dow, J. and Werlang, S. (1994a) Learning under Knightian uncertainty: the law of large numbers for non-additive probabilities. Mimeo, London School of Business.
45. Dow, J. and Werlang, S. (1994b) Nash equilibrium under Knightian uncertainty: breaking down backward induction. Journal of Economic Theory 64(2): 305-324.
46. Du, N. and Budescu, D. (2005) The effects of imprecise probabilities and outcomes in evaluating investment options. Management Science 51: 1791-1803.
47. Eichberger, J. and Kelsey, D. (1999) E-capacities and the Ellsberg paradox. Theory and Decision 46: 107-138.
48. Eichberger, J. and Kelsey, D. (2002) Strategic complements, substitutes, and ambiguity: the implications for public goods. Journal of Economic Theory 106: 436-466.
49. Eichberger, J., Kelsey, D. and Schipper, B.C. (2009) Ambiguity and social interaction. Oxford Economic Papers 61: 355-379.
50. Ellsberg, D. (1961) Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics 75: 643-669.
51. Epstein, L. (1999) A definition of uncertainty aversion. Review of Economic Studies 66: 579-608.
52. Epstein, L. (2009) Three paradoxes for the smooth ambiguity model of preference. Mimeo, Boston University.
53. Epstein, L. and LeBreton, M. (1993) Dynamically consistent beliefs must be Bayesian. Journal of Economic Theory 61(1): 1-22.
54. Epstein, L., Marinacci, M. and Seo, K. (2007) Coarse contingencies and ambiguity. Theoretical Economics 2: 355-394.
55. Epstein, L. and Miao, J. (2003) A two-person dynamic equilibrium under ambiguity. Journal of Economic Dynamics and Control 27: 1253-1288.
56. Epstein, L. and Schneider, M. (2003a) IID: independently and indistinguishably distributed. Journal of Economic Theory 113: 32-50.
57. Epstein, L. and Schneider, M. (2003b) Recursive multiple prior. Journal of Economic Theory 113: 1-31.
58. Epstein, L. and Schneider, M. (2007) Learning under Ambiguity. Review of Economic Studies 74: 1275-1303.
59. Epstein, L. and Schneider, M. (2008) Ambiguity, information quality and asset pricing. Journal of Finance 63: 197-228.
60. Epstein, L. and Seo, K. (2009a) A de Finetti theorem for capacities: ambiguity about correlation. Mimeo.
61. Epstein, L. and Seo, K. (2009b) Symmetry of evidence without evidence of symmetry. Mimeo.
62. Epstein, L. and Wang, T. (1994) Intertemporal asset pricing under Knightian uncertainty. Econometrica 62(3): 283-322.
63. Epstein, L. and Zhang, J. (2001) Subjective probabilities on subjectively unambiguous events. Econometrica 69: 265-306.
64. Epstein, L. and Zin, S. (1989) Substitution, risk aversion and the temporal behavior of consumption and asset returns: a theoretical framework. Econometrica 57: 937-969.
65. Ergin, A. and Gul, F. (2009) A theory of subjective compound lotteries. Journal of Economic Theory 144(3): 899-929.
66. Fox, C. and Tversky, A. (1995) Ambiguity aversion and comparative ignorance. Quarterly Journal of Economics 110: 585-603.
67. Gajdos, T., Hayashi, T., Tallon, J.-M. and Vergnaud, J.-C. (2008) Attitude toward imprecise information. Journal of Economic Theory 140: 23-56.
68. Ghirardato, P. (2001) Coping with ignorance: unforeseen contingencies and non-additive uncertainty. Economic Theory 17: 247-276.
69. Ghirardato, P. (2002) Revisiting savage in a conditional world. Economic Theory 20: 83-92.
70. Ghirardato, P. and Marinacci, M. (2001) Risk, ambiguity, and the separation of utility and beliefs. Mathematics of Operations Research 26: 864-890.
71. Ghirardato, P. and Marinacci, M. (2002) Ambiguity aversion made precise: a comparative foundation and some implications. Journal of Economic Theory 102: 251-282.
72. Ghirardato, P., Maccheroni, F. and Marinacci, M. (2004) Differentiating ambiguity and ambiguity attitude. Journal of Economic Theory 118: 133-173.
73. Gilboa, I. (2009) Theory of Decision under Uncertainty, Econometric Society Monographs edn. Cambridge: Cambridge University Press.
74. Gilboa, I. and Schmeidler, D. (1989) Maxmin expected utility with a non-unique prior. Journal of Mathematical Economics 18: 141-153.
75. Gilboa, I. and Schmeidler, D. (1993) Updating ambiguous beliefs. Journal of Economic Theory 59(1): 33-49.
76. Gilboa, I., Maccheroni, F., Marinacci, M. and Schmeidler, D. (2008a) Objective and subjective rationality in a multiple prior model. Working Paper 73, Collegio Carlo Alberto.
77. Gilboa, I., Postlewaite, A. and Schmeidler, D. (2008b) Probabilities in economic modeling. Journal of Economic Perspectives 22: 173-188.
78. Grant, S. and Quiggin, J. (2005) Increasing uncertainty: a definition. Mathematical Social Sciences 49: 117-141.
79. Guiso, L. and Jappelli, T. (2008) The role of intuition and reasoning in driving aversion to risk, aversion to ambiguity and regret. Mimeo.
80. Halevy, Y. (2007) Ellsberg revisited: an experimental study. Econometrica 75: 503-536.
81. Haller, H. (2000) Non-additive beliefs in solvable games. Theory and Decision 49: 313-338.
82. Hammond, P. (1988) Consequentialist foundations for expected utility. Theory and Decision 25: 25-78.
83. Hanany, E. and Klibanoff, P. (2009) Updating ambiguity averse preferences. Mimeo, Northwestern University.
84. Hansen, L. and Sargent, T. (2001) Robust control and model uncertainty. American Economic Review 91: 60-66.
85. Hansen, L. and Sargent, T. (2008) Robustness. Princeton University Press: Princeton.
86. Hayashi, T. (2005) Intertemporal substitution, risk aversion and ambiguity aversion. Economic Theory 25(4): 933-956.
87. Hayashi, T. and Wada, R. (2010) Choice with imprecise information: an experimental approach. Theory and Decision 69(3): 355-373.
88. Heath, C. and Tversky, A. (1991) Preference and beliefs: ambiguity and competence in choice under uncertainty. Journal of Risk and Uncertainty 4: 5-28.
89. Hey, J., Lotito, G. and Maffioletti, A. (2008) The descriptive and predictive adequacy of theories of decision making under uncertainty/ambiguity. Mimeo.
90. Hogarth, R. and Kunreuther, H. (1985) Ambiguity and insurance decisions. American Economic Review 75: 386-390.
91. 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.
92. Jaffray, J.-Y. (1989) Linear utility for belief functions. Operations Research Letters 8: 107-112.
93. Jaffray, J.-Y. (1994) Dynamic Decision Making with Belief Functions (pp. 331-352). New York, NY, USA: John Wiley & Sons, Inc.
94. Jaffray, J.-Y. and Jeleva, M. (2009) How to deal with partially analyzable acts? Theory and Decision, in press.
95. Jaffray, J.-Y. and Philippe, F. (1997) On the existence of subjective upper and lower probabilities. Mathematics of Operations Research 22: 165-185.
96. Jeleva, M. and Rossignol, S. (2009) How to represent imprecise information? A review of some statistical tools. Mimeo, U. Paris I.
97. Kahneman, D. and Tversky, A. (1979) Prospect theory: an analysis of decision under risk. Econometrica 47: 263-291.
98. Kahneman, D. and Tversky, A. (1992) Advances in prospect theory: cumulative representation of uncertainty. Journal of Risk and Uncertainty 5: 297-323.
99. Keller, R., Sarin, R. and Sounderpandian, J. (2007) An examination of ambiguity aversion. Judgment and Decision Making 5: 390-397.
100. Kelsey, D. and Eichberger, J. (2000) Non-additive beliefs and strategic equilibria. Games and Economic Behaviour 30: 183-215.
101. Klibanoff, P., Marinacci, M. and Mukerji, S. (2005) A smooth model of decision making under uncertainy. Econometrica (6): 1849-1892.
102. Klibanoff, P., Marinacci, M. and Mukerji, S. (2009a) On the smooth ambiguity model: a reply. Mimeo, Northwestern University.
103. Klibanoff, P., Marinacci, M. and Mukerji, S. (2009b) Recursive smooth ambiguity preferences. Journal of Economic Theory (3): 930-976.
104. Kozhan, R. and Salmon, M. (2009) Uncertainty aversion in a heterogeneous agent model of foreign exchange rate formation. Journal of Economic Dynamics and Control (5): 1106-1122930-976.
105. Kreps, D. (1979) A representation theorem for preference for flexibility. Econometrica 47: 565-576.
106. Kreps, D. and Porteus, E. (1978) Temporal resolution of uncertainty and dynamic choice theory. Econometrica 46: 185-200.
107. Kunreuther, H., Hogarth, R. and Meszaros, J. (1993) Insurer ambiguity and market failure. Journal of Risk and Uncertainty 7: 71-87.
108. Lauriola, M. and Levin, I. (2001) Relating individual differences in attitude toward ambiguity to risky choices. Journal of Behavioral Decision Making 14: 107-122.
109. Leippold, M., Trojani, F. and Vanini, P. (2008) Learning and asset prices under ambiguous information. Review of Financial Studies 21: 2565-2597.
110. Liu, H. and Colman, A. (2009) Ambiguity aversion in the long run: repeated decisions under risk and uncertainty. Journal of Economic Psychology 30: 277-284.
111. Lo, K. (1998) Sealed bid auctions with uncertainty averse bidders. Economic Theory 12(1): 1-20.
112. Ludwig, A. and Zimper, A. (2006) Investment behavior under ambiguity: the case of pessimistic decision makers. Mathematical Social Sciences 52: 111-130.
113. Maccheroni, F., Marinacci, M. and Rustichini, A. (2005) Ambiguity aversion, robustness, and the variational representation of preferences. Econometrica 74: 1447-1498.
114. Machina, M. (1989) Dynamic consistency and non-expected utility models of choice under uncertainty. Journal of Economic Literature 28: 1622-1668.
115. Machina, M. and Schmeidler, D. (1992) A more robust definition of subjective probability. Econometrica 60: 745-780.
116. Maffioletti, A. and Schmidt, U. (2008) The effect of the elicitation method on ambiguity aversion: an experimental investigation. Working Paper.
117. Marinacci, M. (1999) Limit laws for non-additive probabilities, and their frequentist interpretation. Journal of Economic Theory 84: 145-195.
118. Marinacci, M. (2000) Ambiguous games. Games and Economic Behavior 31: 191-219.
119. McClennen, E. (1990) Rationality and Dynamic Choice Foundational Explorations. Cambridge: Cambridge University Press.
120. Mukerji, S. and Tallon, J.-M. (2001) Ambiguity aversion and incompleteness of financial markets. Review of Economic Studies 68: 883-904.
121. Nau, B. (2006) Uncertainty aversion with second-order utilities and probabilities. Management Science 52: 136-145.
122. Nehring, K. (2000) A theory of rational decision under ignorance. Theory and Decision 48: 205-240.
123. Nehring, K. (2001) Ambiguity in the context of probabilistic beliefs. Working Paper.
124. Potamites, E. and Zhang, B. (2007) Measuring ambiguity attitudes: a field experiment among small-scale stock investors in China. Mimeo, New York University.
125. Quiggin, J. (1982) A theory of anticipated utility. Journal of Economic Behavior and Organization 3: 323-343.
126. Raiffa, H. (1961) Risk, ambiguity, and the Savage axioms: comment. Quarterly Journal of Economics 75: 690-694.
127. Rigotti, L. and Shannon, C. (2005) Uncertainty and risk in financial markets. Econometrica 73: 203-243.
128. Rigotti, L., Shannon, C. and Strzalecki, T. (2008) Subjective beliefs and ex-ante trade. Econometrica 76: 1167-1190.
129. Rinaldi, F. (2009) Endogenous incompleteness of financial markets: the role of ambiguity and ambiguity aversion. Journal of Mathematical Economics 45: 872-893.
130. Rothschild, M. and Stiglitz, J. (1970) Increasing risk I: a definition. Journal of Economic Theory 2: 225-243.
131. Routledge, B. and Zin, S. (2009) Model uncertainty and liquidity. Review of Economic Dynamics 12(4).
132. Salo, A. and Weber, M. (1995) Ambiguity aversion in first price sealed-bid auctions. Journal of Risk and Uncertainty 11: 123-137.
133. Savage, L. (1954) The Foundations of Statistics. New-York: John Wiley.
134. Schmeidler, D. (1989) Subjective probability and expected utility without additivity. Econometrica 57(3): 571-587.
135. Segal, U. (1987) The Ellsberg paradox and risk aversion: an anticipated utility approach. International Economic Review 28: 175-202.
136. Segal, U. (1990) Two-stage lotteries without the reduction axiom. Econometrica 58: 349-377.
137. Seo, K. (2009) Ambiguity and second-order belief. Econometrica 77(5): 1575-1605.
138. Siniscalchi, M. (2009) Vector expected utility and attitudes toward variation. Econometrica 77(3): 801-855.
139. Skiadas, C. (1998) Recursive utility and preferences for information. Economic Theory 12: 293-312.
140. Snow, A. (2010) Ambiguity and the value of information. Journal of Risk and Uncertainty 40(2): 133-145.
141. Trautmann, S., Vieider, F. and Wakker, P. (2009) Preference reversals for ambiguity aversion. Working paper, Department of Economics, Erasmus University, Rotterdam.
142. Treich, N. (2010) The value of a statistical life under ambiguity aversion. Journal of Environmental Economics and Management 59: 15-26.
143. Turocy, T.L. (2008) Auction choice for ambiguity-averse sellers facing strategic uncertainty. Games and Economic Behavior 62: 155-179.
144. Vierø, M.-L. (2009) Exactly what happens after the Anscombe-Aumann race? Representing preferences in vague environments. Economic Theory 41: 175-212.
145. Viscusi, W. and Chesson, H. (1999) Hopes and fears: the conflicting effects of risk ambiguity. Theory and Decision 47: 153-178.
146. Viscusi, W. and Magat, W. (1992) Bayesian decisions with ambiguous belief aversion. Journal of Risk and Uncertainty 5: 371-387.
147. Viscusi, W., Magat, W. and Hubert, H. (1991) Communication of ambiguous risk information. Theory and Decision 31: 159-173.
148. Viscusi, W., Magat, W. and Hubert, H. (1999) Smoking status and public responses to ambiguous scientific risk evidence. Southern Economic Journal 66(2).
149. von Neumann, J. and Morgenstern, O. (1947) Theory of Games and Economic Behavior. Princeton: Princeton University Press.
150. Wakker, P. (1990) Characterizing optimism and pessimism directly through comonotonicity. Journal of Economic Theory 52: 453-463.
151. Wakker, P. and Tversky, A. (1993) An axiomatization of cumulative prospect theory. Journal of Risk and Uncertainty 7: 147-176.
152. Wang, T. (2003) A class of multi-prior preferences. Discussion Paper, University British Columbia.
153. Yaari, M. (1969) Some remarks on measures of risk aversion and on their uses. Journal of Economic Theory 1: 315-329.
154. Yates, F. and Zukowski, L. (1976) Characterization of ambiguity in decision making. Behavioral Science 21: 19-25.