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The Recent Advances in Decision Theory Under Uncertainty

a non-technical introduction

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Abstract

Decision theory under uncertainty (from now on DT) has played a remarkable role in many scientific disciplines such as economics, management, sociology, political science, law, philosophy, psychology, biology, even physics1. Any scientific discipline involves a relationship between an observer and an object of study. DT may often intervene in order to clarify the influence of the observer on her object, or at least on its description, explanation, and forecast. More in general, inductive (or abductive) inferences based on empirical evidence are often guided by procedures and criteria which are decision-theoretic, or may be rephrased in these terms. In the social sciences, even the object of the analysis is often taken to be, or to be reducible to, a set of past, present, or prospective, individual or collective decisions. Though the impact of DT has been deep in many scientific disciplines, it is safe to say that it has been, and is more and more, remarkable in economics (Anand (1993, p.l)). Not by chance, many of its main contributors in this century, have been either economists (Knight, Keynes, Morgenstern, Allais, Shackle, Ellsberg, Quiggin, Yaari, Kreps, etc.) or scholars with a strong interest in economics (Ramsay, de Finetti, {ptvon} Neumann, Savage, Aumann, Machina, Schmeidler, Epstein, Gilboa, etc.).

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References

  • Allais, M., (1953), Le comportement de l’homme rationnel devant le risque: critique des postulats et axiomes de l’école américaine, Econometrica, 21, pp.503–546.

    Article  Google Scholar 

  • Anand, P., (1991), Foundations of rational choice under risk, Oxford, Clarendon Press.

    Google Scholar 

  • Anscombe, F.J., and Aumann R., (1963), A Definition of Subjective Probability, Annals of Mathematical Statistics, 34, pp.199–205.

    Article  Google Scholar 

  • Arrow, K. J., (1957), Statistics and Economic Policy, Econometrica, 25, pp.523–531.

    Article  Google Scholar 

  • Arrow, K. J., (1964), The Role of Securities in the Optimal Allocation of Risk-Bearing, Review of Economic Studies, 31, pp.91–96.

    Article  Google Scholar 

  • Arrow, K.J., (1968), Optimal Capital Policy with Irreversible Investment, in J. Wolfe, ed., Value. Capital, and Growth, Chicago University Press, pp. 1–20.

    Google Scholar 

  • Arrow, K. J., (1971), Essays in the theory of risk-bearing, North-Holland, Amsterdam.

    Google Scholar 

  • Arrow, K. J., and A Fisher, (1974), Environmental Preservation, Uncertainty and Irreversibility, Quarterly Journal of Economics, 89, pp.312–319.

    Article  Google Scholar 

  • Arrow, K. J., and L. Hurwicz, (1972), Optimality criterion for decision-making under ignorance, in Carter C.F., Ford J.L., eds., Uncertainty and Expectations in Economics, Oxford, Basil Blackwell, pp.1–11.

    Google Scholar 

  • Arrow, K. J., and M. Kurz, (1970), Optimal Growth with Irreversible Investment in a Ramsey Model, Econometrica, 38, pp.341–344.

    Article  Google Scholar 

  • Arrow, K. J., and R. Lind, (1970), Uncertainty and the Evaluation of Public Investment Decisions, American Economic Review, 60, pp.364–378.

    Google Scholar 

  • Barret, C. R., and Pattanaik, P.K., (1986), Decision making under complete uncertainty: the ordinal framework, in S. Seu, ed., Uncertainty in Economic Life.

    Google Scholar 

  • Basili, M. and A. Vercelli, (1998), Environmental option value: a critical assessment, in M. Dore and T. Maount, eds., Global Environmental Economics: Equity and the limits to markets, Oxford, Blackwell.

    Google Scholar 

  • Begg, D. K. H., (1982), The Rational Expectations Revolution in Macroeconomics, Allan, Oxford.

    Google Scholar 

  • Bernanke, P., (1983), Irreversibility, Uncertainty and Cyclical Investment, Quarterly Journal of Economics, 98, pp.85–106.

    Article  Google Scholar 

  • Bewley, T. F., (1986), Knightian Decision Theory: Part 1, Cowles Foundation Discussion Paper n°807 (New Haven, CT).

    Google Scholar 

  • Billot, A., (1992), From fuzzy set theory to non-additive probabilities: How have economists reacted?, Fuzzy Sets and Systems, 49, pp.75–90.

    Article  Google Scholar 

  • Binmore, K. G., (1986), Remodelled rational players, Discussion Paper, London School of Economics, London.

    Google Scholar 

  • Bray, M., (1982), Learning, Estimation, and the Stability of Rational Expectations Equilibria, Journal of Economic Theory, 26, pp.313–317.

    Article  Google Scholar 

  • Bray, M., and N. E. Savin, (1986), Rational Expectations Equilibria, Learning and Model Specification, Econometrica, 54, pp. 129–160.

    Article  Google Scholar 

  • Brun, W., and K. Teigen, (1990), Prediction and Postdiction Inferences in Guessing, Journal of Behavioural Decision Making, 3, pp.17–28.

    Article  Google Scholar 

  • Caballero, R., (1991), On the Sign of the Investment-Uncertainty Relationship, American Economic Review, 81, pp.279–288.

    Google Scholar 

  • Camerer, C., M. Weber, (1992), Recent Developments in Modelling Preferences: Uncertainly and Ambiguity, Journal of Risk and Uncertainty, 5, pp.325–370.

    Article  Google Scholar 

  • Chateauneuf, A., Kast, R., Lapied, A., (1992a), Choquet Pricing for Financial Markets with Frictions, mimeo.

    Google Scholar 

  • Chateauneuf, A., (1992b), Pricing in Slack Markets, Document de Travail GREQE, n°92A05.

    Google Scholar 

  • Chateauneuf, A., Jaffray, J. Y., (1989), Some characterisations of lower probabilities and other monotone capacities through the use of Möbius inversion, Math. Social Sciences, 17, pp. 263–283.

    Article  Google Scholar 

  • Cohendet, P., and P. Llerena, eds., (1989), Flexibility. Information et decision, Paris, Economica.

    Google Scholar 

  • Choquet, G., (1953–4), Theory of Capacities, Annales de l’Institut Fourier, 5, pp.131–295.

    Article  Google Scholar 

  • Curley, S. P., M.J. Young, R.A. Abrams, (1986), Psychological Sources of Ambiguity Avoidance, Organisational Behaviour and Human Decision Processes, 38, pp.230–256.

    Article  Google Scholar 

  • De Canio, S. J., (1979), Rational Expectations and Learning from Experience, Quarterly Journal of Economics, 93, pp.47–58.

    Article  Google Scholar 

  • De Finetti, B., (1937), La Prevision: Ses Lois Logiques, Ses Sources Subjectives, Annales de l’Institute Henry Poincaré, 7, pp.1–68. English translation: Foresight: Its Logical Laws. Its Subjective Sources, in Kyburg-Smokler, (1980), pp.93-158.

    Google Scholar 

  • Dempster, A. P., (1967), Upper and lower probabilities induced by a multivalued mapping, Ann Math. Statist., 38, pp.325–339.

    Article  Google Scholar 

  • Diaconis, P., and Freedman D., (1986), On the consistency of Bayes estimates, The Annals of Statistics, 14,1, pp.1–26.

    Article  Google Scholar 

  • Diamond, P., (1980), An Alternative to Steady State Comparison, Economic Letters, 5, pp.7–9.

    Article  Google Scholar 

  • Diamond, P., (1982a), A Search-Equilibrium Approach to the Micro Foundation of Macroeconomics, M.I.T. Press, Cambridge, Massachusetts.

    Google Scholar 

  • Diamond, P., (1982b), Aggregate Demand Management in Search-Equilibrium, Journal of Political Economy, 90, pp.881–894.

    Article  Google Scholar 

  • Diamond, P., (1984), Money in Search-Equilibrium, Econometrica, 52, pp. 1–20.

    Article  Google Scholar 

  • Dow, J., Werlang, S. R. C., (1992a), Excess volatility of stock prices and Knightian uncertainty, European Economic Review, 36, pp.631–638.

    Article  Google Scholar 

  • Dow, J., (1992b), Uncertainty aversion, risk aversion, and the optimal choice of portfolio, Econometrica. 60, pp. 197–204.

    Article  Google Scholar 

  • Dow, J., (1992c), The ex-ante non-optimality of the Dempster-Shafer rule for ambiguous beliefs, EPGE Fundaçao Getulio Vargas, working paper n.185.

    Google Scholar 

  • Dubois, D., (1980), Un economiste precurseur de la theorie des possibilites: G.L.S. Shackle, Busefal, 2, pp.70–73.

    Google Scholar 

  • Ellsberg, D., (1961), Risk, ambiguity, and the Savage axioms, Quarterly Journal of Economics, 75, pp.643–669.

    Article  Google Scholar 

  • Elster, J., (1979), Ulysses and the Sirens. Studies in rationality and irrationality, Cambridge University Press.

    Google Scholar 

  • Epstein, L., (1980), Decision Making and Temporal Resolution of Uncertainty, International Economic Review, 21, pp.269–283.

    Article  Google Scholar 

  • Epstein, L., and Le Breton, (1993), Dynamically Consistent Beliefs Must Be Bayesian, Journal of Economic Theory, 61, pp. 1–22.

    Article  Google Scholar 

  • Evans, G. W., (1983), The Stability of Rational Expectations in Macroeconomic Models, in R. Frydman, E.S. Phelps, eds., Individual Forecasting and Aggregate Outcomes. ‘Rational’ Expectations Examined, Cambridge University Press, Cambridge.

    Google Scholar 

  • Evans, G. W., and S. Honkapohja, (1990), Learning, convergence, and stability with multiple rational expectations equilibria, STICERD Discussion Paper, London.

    Google Scholar 

  • Favereau, O., (1989), Valeur d’option et flexibilité: de la rationalité substantielle a la rationalité procedurale, in P. Cohendet, P. Llerena, eds., (1989).

    Google Scholar 

  • Fellner, W., (1961), Distortion of Subjective Probabilities as a Reaction to Uncertainty, Quarterly Journal of Economics, 75, pp.670–694.

    Article  Google Scholar 

  • Feynman, R. P., et al., eds., (1963), The Feynman Lectures on Physics, vol.1, pp.643–669.

    Google Scholar 

  • Fishburn, P. C., (1988), Non-linear preferences and utility theory, Baltimore, John Hopkins University Press.

    Google Scholar 

  • Fisher, A., M. Hanemann, (1987), Quasi-Option Value: Some Misconceptions Dispelled, Journal of Environmental Economics and Management, 14, pp.183–190.

    Article  Google Scholar 

  • Fourgeaud, C., C. Gourieroux, J. Pradel, (1986), Learning Procedure and Convergence to Rationality, Econometrica, 54, pp.845–868.

    Article  Google Scholar 

  • Feixas, X., (1986), L’effet-irreversibilite generalise, in Boiteux M., De Montbrial T., Munier B., eds., Marchés, Capital et Incertitude. Essais en l’honneur de Maurice Allais, Paris, Economica.

    Google Scholar 

  • Feixas, J. J. Laffont, (1984), On the irreversibility effect, in Boyer M., R.E. Kihistrom, eds., Bayesian models in economic theory, North-Holland, Amsterdam, pp.105–114.

    Google Scholar 

  • Frisch, D., and J. Baron, (1988), Ambiguity and Rationality, Journal of Behavioural Decision Making, 1, pp.149–157.

    Article  Google Scholar 

  • Gärdenfors, P., and Sahlin N. E., (1982), Unreliable Probabilities, Risk Taking, and Decision making, Synthèse, 53, pp.361–386.

    Article  Google Scholar 

  • Ghirardato, P., (1994), Coping with Ignorance: Unforeseen Contingencies and Nonadditive Uncertainty, Discussion Paper, Department of Economics, Berkeley.

    Google Scholar 

  • Gilboa, I., (1987), Expected Utility with Purely Subjective Non-Additive Probabilities, Journal of Mathematical Economics, 16, pp.65–68.

    Article  Google Scholar 

  • Gilboa, I., (1989), Additivizations of Nonadditive Measures, Mathematics of Operation Research, 4, pp.1–17.

    Article  Google Scholar 

  • Gilboa, I., and Schmeidler D., (1989), Maximin expected utility with a non-unique prior, Journal of Mathematical Economics, 18, pp.141–153.

    Article  Google Scholar 

  • Gilboa, I., (1993), Updating Ambiguous Beliefs, Journal of Economic Theory, 59, pp.33–49.

    Article  Google Scholar 

  • Gilboa, I., (1994), Case-based Decision Theory, mimeo.

    Google Scholar 

  • Goldman, M., (1974), Flexibility and the Demand for Money, Journal of Economic Theory, 9, pp.203–222.

    Article  Google Scholar 

  • Goldman, M., (1978), Portfolio Choice and Flexibility, Journal of Monetary Economics, 4, pp.263–279.

    Article  Google Scholar 

  • Hahn, F., (1990), Liquidity, in Hahn-Friedman, ed., Handbook of Monetary Economics. Amsterdam, North-Holland, pp.63–80.

    Chapter  Google Scholar 

  • Hammond, P., (1976), Changing tastes and coherent dynamic choice, Review of Economic Studies, 43, pp.159–173.

    Article  Google Scholar 

  • Hammond, P., (1988), Consequentialism and the independence axiom, in B. Munier, ed., Risk, Decision and Rationality, D. Reidel Publ. Co., Amsterdam, pp.503–516.

    Chapter  Google Scholar 

  • Hammond, P., (1989), Consistent plans, consequentialism and expected utility, Econometrica, 57,6, pp.1445–1449.

    Article  Google Scholar 

  • Hanemann, M., (1989), Information and the Concept of Option Value, Journal of Environmental Economics and Management, 16, pp.23–37.

    Article  Google Scholar 

  • Hart, A. G., (1942), Risk, Uncertainty, and the Unprofitability of Compounding Probabilities, in Lange O., Mclntyre F., and T.O. Yntema, eds., Studies in Mathematical Economics and Econometrics, Chicago, Chicago University Press.

    Google Scholar 

  • Heath, C., and A. Tversky, (1991), Preference and Belief Ambiguity and Competence in Choice under Uncertainty, Journal of Risk and Uncertainty, 4, pp.5–28.

    Article  Google Scholar 

  • Henry, C., (1974a), Option Values in the Economics of Irreplaceable Assets, Review of Economic Studies, 41, pp.89–104.

    Article  Google Scholar 

  • Henry, C., (1974b), Investment Decision Under Uncertainty: the Irreversible effect, American Economic Review, 64, pp. 1006–1012.

    Google Scholar 

  • Hicks, J., (1974), The Crisis in Keynesian Economics, New York, Basic Books.

    Google Scholar 

  • Hogart, R. M., and H. J. Einhorn, (1990), Venture Theory: A Model of Decision Weights. Management Science, 36, pp.780–803.

    Article  Google Scholar 

  • Jaffray, J.Y., and P. Wakker, (1994), Decision making with belief functions: compatibility and incompatibility with the sure-thing principle, Journal of Risk and Uncertainty, 8, pp.255–271.

    Google Scholar 

  • Jones, R., and J. Ostroy, (1984), Flexibility and Uncertainty, Review of Economic Studies, 51, pp. 13–32.

    Article  Google Scholar 

  • Kelsey, D., and Quiggin J., (1992), Theories of choice under ignorance and uncertainty, Journal of Economic Surveys, vol.6, n.2, pp.133–153.

    Article  Google Scholar 

  • Keppe, H.J., and M. Weber, (1991), Judged Knowledge and Ambiguity Aversion, Working Paper n. 277, Christian Albrechts Universitat, Kiel, Germany.

    Google Scholar 

  • Keynes, J. M., (1936), The General Theory of Employment. Interest and Money, London, Macmillan.

    Google Scholar 

  • Knight, F., (1921), Risk, Uncertainty and Profit, Houghton Mifflin, New York.

    Google Scholar 

  • Koopmans, T. C., (1964), On flexibility of future preferences, in Shelly M., G. Bryan, eds., Human judgements and optimality, Wiley, pp.243–254.

    Google Scholar 

  • Kreps, D., (1979), A representation theorem for preference for flexibility, Econometrica, 47, pp.565–577.

    Article  Google Scholar 

  • Kreps, D.M., (1988), Notes on the Theory of Choice, Boulder, Westview Press.

    Google Scholar 

  • Kurz, M., (1974), The Kesten-Stigum Model and the Treatment of Uncertainty in Equilibrium Theory, in M.C. Balch, D.M. McFadden, andS. Wu (eds.), Essays in Economic Behaviour Under Uncertainty, Amsterdam, North Holland.

    Google Scholar 

  • Kurz, M., (1991a), On rational belief equilibria, Discussion Paper, Stanford University.

    Google Scholar 

  • Kurz, M., (1991b), On the Structure and Diversity of Rational Beliefs, Discussion Paper, Stanford University.

    Google Scholar 

  • Kurz, M., (1993), Rational preferences and rational beliefs, manuscript.

    Google Scholar 

  • Kyburg, H. E. Jr., and Smokier H.E., eds., (1964), Studies in Subjective Probability, Wiley and Sons, New York.

    Google Scholar 

  • Lippman, S., and J. McCall, (1986), An Operational Measure of Liquidity, American Economic Review, 76, pp.43–55.

    Google Scholar 

  • Lucas, Jr., R. E., (1978), Asset Prices in an Exchange Economy, Econometrica, 46, pp. 1429–1445.

    Article  Google Scholar 

  • Lucas, Jr., (1986), Adaptive Behaviour and Economic Theory, Journal of Business, 59, Supplement, pp.5401–5426.

    Google Scholar 

  • Machina, M. J., (1982), ‘Expected Utility’ analysis without the independence axiom, Econometrica 50(2), pp.277–323.

    Article  Google Scholar 

  • Machina, M. J., (1987), Choice Under Uncertainty: Problems Solved and Unsolved, Journal of Economic Perspectives, 1, pp.121–154.

    Article  Google Scholar 

  • Machina, M. J. and Schmeidler D., (1992), A more robust definition of subjective probability, Econometrica, 60(4), pp.745–780.

    Article  Google Scholar 

  • Makower, H., and T. Marschak, (1938), Assets, Prices and Monetary Theory, Economica, 5, pp.261–288.

    Article  Google Scholar 

  • Marcet, A., and T. J. Sargent, (1988), The Fate of Systems with ‘Adaptive’ Expectations, American Economic Review.Papers and Proceedings, 78, pp.168–172.

    Google Scholar 

  • Marcet, A., (1989a), Convergence of Least Squares Learning Mechanisms in Self-Referential Stochastic Models, Journal of Economic Theory, 48, pp.337–368.

    Article  Google Scholar 

  • Marcet, A., (1989b), Convergence of Least Squares Learning in Environments with Hidden State Variables and Private Information, Journal of Political Economy,97, pp. 1306–1322.

    Article  Google Scholar 

  • Marschak, T., (1938), Money and Theory of Asset, Econometrica, 6, pp.311–335.

    Article  Google Scholar 

  • Marschak, T., (1949), Role of Liquidity under Complete and Incomplete Information, American Economic Review, 39, pp.182–195.

    Google Scholar 

  • Marschak, T., and K. Miyasawa, (1968), Economic Comparability of Information Systems, International Economic Review, 9, pp.137–174.

    Article  Google Scholar 

  • Marschak, T., and R. Nelson, (1962), Flexibility, Uncertainty and Economic Theory, Metroeconomica, 14, pp.42–58.

    Article  Google Scholar 

  • Miller, J. R., and F. Lad, (1984), Flexibility, learning, and irreversibility in environmental decisions: a Bayesian approach, J. of Environ. Econ. and Manag., 11, pp.161–172.

    Article  Google Scholar 

  • Montesano, A., (1991), Measures of Risk Aversion with Expected and Nonexpected Utility, Journal of Risk and Uncertainty, 4, pp.271–283.

    Article  Google Scholar 

  • Montesano, A., (1993), Non-Additive Probabilities and the Measure of Uncertainty and Risk Aversion, mimeo.

    Google Scholar 

  • von Neumann, J., and Morgenstern O., (1944), Theory of games and Economic Behaviour, Princeton University Press, Princeton.

    Google Scholar 

  • Pindyck, R., (1988), Irreversible Investment, Capacity Choice, and the Value of the Firm, American Economic Review, 78, pp.969–985.

    Google Scholar 

  • Pindyck, R., (1991), Irreversibility, Uncertainty, and Investment, Journal of Economic Literature, 29, pp.1110–1148.

    Google Scholar 

  • Ponsard, C., (1986), Foundations of soft decision theory, in J. Kacprzyl and R.R. Yeger (eds.), Management Decision Support Systems Using Fuzzy Sets and Possibility Theory, Köln, Verlag TUV.

    Google Scholar 

  • Quiggin, J., (1982), A theory of anticipated utility, Journal of Economic Behaviour and Organisation, 3(4), pp.323–343.

    Article  Google Scholar 

  • Sargent, T. J., (1993), Bounded Rationality in Macroeconomics, MIT Press, Boston.

    Google Scholar 

  • Sarin, R., and P. Wakker, (1992), A Simple Axiomatization of Non-additive Expected Utility, Econometrica, 60, pp. 1255–1272.

    Article  Google Scholar 

  • Savage, L. J., (1954), The Foundations of Statistics, John Wiley and Sons, New York. Revised and enlarged edition, Dover, New York, (1972).

    Google Scholar 

  • Schmeidler, D., (1982), Subjective probability without additivity, Working Paper, Forder Institute for Economic Research, Tel Aviv University.

    Google Scholar 

  • Schmeidler, D., (1986), Integral representation without additivity, Proceedings of the American Mathematical Society, 97,2, pp.255–261.

    Article  Google Scholar 

  • Schmeidler, D., (1989), Subjective probability and expected utility without additivity, Econometrica, 57, pp.571–587.

    Google Scholar 

  • Segal, U., (1987), The Ellsberg paradox and risk aversion: An anticipated utility approach, International Economic Review, 28(1), pp. 175–202.

    Article  Google Scholar 

  • Shackle, G. L. S., (1952), Expectations in Economics, Cambridge, Cambridge University Press.

    Google Scholar 

  • Shafer, G., (1976), A Mathematical Theory of Evidence, Princeton, Princeton University Press.

    Google Scholar 

  • Shafer, G., (1978), Non-additive probabilities in the works of Bernoulli and Lambert, Arch. Hist. Exact. Sci., 19, pp.309–370.

    Article  Google Scholar 

  • Shafer, G., (1985), Conditional Probability, International Statistical Review, 53, pp.261–277.

    Article  Google Scholar 

  • Simon, H. A., (1956), Dynamic Programming Under Uncertainty with a Quadratic Criterion function, Econometrica, 24, pp.74–81.

    Article  Google Scholar 

  • Simon, H. A., (1982), Models of Bounded Rationality, MIT Press, Cambridge (Mass).

    Google Scholar 

  • Simonsen, I. H., Verlang, S. R. C., (1991), Sub-additive probabilities and portfolio inertia, Revista de Econometria, 11, pp. 1–19.

    Google Scholar 

  • Strotz, R H., (1956), Myopia and inconsistency in dynamic utility maximisation, Review of Economic Studies, 23, pp.165–180.

    Article  Google Scholar 

  • Theil, H., (1957), A Note on Certainty Equivalence in Dynamic Planning, Econometrica, 25, pp.346–349.

    Article  Google Scholar 

  • Tobin, J., (1958), Liquidity Preference as Behaviour Toward Risk, Review of Economic Studies, 25, pp.65–86.

    Article  Google Scholar 

  • Vercelli, A., (1991), Methodological foundations of macroeconomics, Keynes and Lucas, Cambridge, Cambridge University Press.

    Book  Google Scholar 

  • Vercelli, A., (1995), From soft uncertainty to hard environmental uncertainty, Economie Appliquée, 48, pp.251–269.

    Google Scholar 

  • Wakker, P., (1989), Continuous Subjective Expected Utility With Non-Additive Probabilities, Journal of Mathematical Economics, 18, pp.1–27

    Article  Google Scholar 

  • Wakker, P., (1990), A behavioural foundation for fuzzy measures, Fuzzy Sets and Systems, 37, pp.327–350.

    Article  Google Scholar 

  • Willinger, M., (1988), The foundations of the theory of choice between experiments, Fourth international conference on the foundations and applications of utility, risk and decision theory, Budapest.

    Google Scholar 

  • Willinger, M., (1989), Flexibilité et valeur de l’information, in P. Cohendet, P. Llerena, eds., pp.103–120.

    Google Scholar 

  • Willinger, M., (1990), Irreversibilité et coherence dynamique des choix, Revue d’Economie Politique, 100,6, pp.808–832.

    Google Scholar 

  • Woodford, M., (1990), Learning to Believe in Sunspots, Econometrica, 58, pp.277–307.

    Article  Google Scholar 

  • Yaari, M., (1987), The dual theory of choice under risk, Econometrica, 55(1), pp.95–115.

    Article  Google Scholar 

  • Zadeh, L.A., (1965), Fuzzy sets, Information and Control, 8, pp.338–353.

    Google Scholar 

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Vercelli, A. (1999). The Recent Advances in Decision Theory Under Uncertainty. In: Luini, L. (eds) Uncertain Decisions. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5083-9_11

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