On the use of capacities in modeling uncertainty aversion and risk aversion

Abstract Schmeidler (1989) and Yaari (1987) have proposed models where attitudes towards uncertainty (or risk) are characterized by not necessarily additive probabilities, and are therefore kept separate from attitudes towards wealth. The axiomatics of both models include a comonotonicity axiom the interpretation of which is delicate. Here, assuming as Yaari that the decision maker displays a constant marginal utility of wealth, we show that the comonotonicity axiom can be significantly weakened while being intuitively meaningful, and that it is dispensable when characterizing some forms of strong uncertainty (or risk) aversion. This investigation is performed within a simpler but possibly more intuitive framework than Schmeidler's and Yaari's.

[1]  Bernd Anger,et al.  Representation of capacities , 1977 .

[2]  Risk aversion without diminishing marginal utility , 1984 .

[3]  L. Hörmander.  Sur la fonction d’appui des ensembles convexes dans un espace localement convexe , 1955 .

[4]  C. Dellacherie.  Quelques Commentaires Sur Les Prolongements De Cafacites , 1971 .

[5]  Josef Hadar,et al.  Rules for Ordering Uncertain Prospects , 1969 .

[6]  P. Wakker.  Continuous subjective expected utility with non-additive probabilities , 1989 .

[7]  T. Fine.  A Note on the Existence of Quantitative Probability , 1971 .

[8]  J. Benzecri,et al.  Théorie des capacités , 1956 .

[9]  Peter P. Wakker,et al.  Under stochastic dominance Choquet-expected utility and anticipated utility are identical , 1990 .

[10]  Uzi Segal.  Anticipated utility: A measure representation approach , 1989 .

[11]  P. J. Huber,et al.  Minimax Tests and the Neyman-Pearson Lemma for Capacities , 1973 .

[12]  J. Quiggin.  A theory of anticipated utility , 1982 .

[13]  Ky Pan.  5. On Systems of Linear Inequalities , 1957 .

[14]  P. Fishburn.  Weak Qualitative Probability on Finite Sets , 1969 .

[15]  C. Berge,et al.  Espaces topologiques : fonctions multivoques , 1966 .

[16]  M. Allais,et al.  Fondements d'une theorie positive des choix comportant un risque et critique des postulats et axiomes de l'ecole americaine , 1959 .

[17]  M. Rothschild,et al.  Increasing risk: I. A definition , 1970 .

[18]  F. J. Anscombe,et al.  A Definition of Subjective Probability , 1963 .

[19]  T. Fine,et al.  Bayes-like Decision Making With Upper and Lower Probabilities , 1982 .

[20]  Leigh Tesfatsion,et al.  Stochastic Dominance and the Maximization of Expected Utility , 1976 .

[21]  L. Shapley.  Cores of convex games , 1971 .

[22]  Heinz J. Skala,et al.  Not Necessarily Additive Realizations of Comparative Probability Relations — A Basis of Decision Theory , 1977 .

[23]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[24]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[25]  D. Schmeidler.  Integral representation without additivity , 1986 .

[26]  D. Schmeidler.  Subjective Probability and Expected Utility without Additivity , 1989 .

[27]  M. Yaari.  The Dual Theory of Choice under Risk , 1987 .

[28]  A. Revuz.  Fonctions croissantes et mesures sur les espaces topologiques ordonnés , 1956 .

[29]  Kennan T. Smith,et al.  Linear Topological Spaces , 1966 .