On expected and von Neumann-Morgenstern utility functions

Metroeconomica, 1978

In this paper we would like to do two things: firstly, to show that the proof of the von-Neumann-Moorgenstern linear utility theorem can be simplified by noting the isomorphism of the problem with Rn secondly, we would like to argue that there is hidden within the von-Neumann-Morgenstern assumptions an unacceptable condition on commodity preferences.

Decision Sciences, 1979

Thirty empirically assessed utility functions on changes in wealth or return on investment were examined for general features and susceptability to fits by linear, power, and exponential functions. Separate fits were made to below-target data and above-target data. The usual “target” was the no-change point.The majority of below-target functions were risk seeking; the majority of above-target functions were risk averse; and the most common composite shape was convex-concave, or risk seeking in losses and risk averse in gains. The least common composite was concave-concave. Below-target utility was generally steeper than above-target utility with a median below-to-above slope ratio of about 4.8. The power and exponential fits were substantially better than the linear fits. Power functions gave the best fits in the majority of convex below-target and concave above-target cases, and exponential functions gave the best fits in the majority of concave below-target and convex above-target cases. Several implications of these results for decision making under risk are mentioned.

SIAM Journal on Optimization, 2013

We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous linear functionals from functional analysis. Our analysis reveals the dual character of utility functions. We also derive new integral representations of dual utility models.

Social Choice and Welfare, 1989

Part I of this paper offers a novel result in social choice theory by extending Harsanyi's well-known utilitarian theorem into a "multi-profile" context. Harsanyi was contented with showing that if the individuals' utilities u~ are von Neumann-Morgenstern, and if the given utility u of the social planner is VNM as well, then the Pareto indifference rule implies that u is affine in terms of the u~. We provide a related conclusion by considering u as functionally dependent on the ul, through a suitably restricted "social welfare functional"

2006

In this paper we extend Savage's theory of decision-making under uncertainty from a classical environment into a non-classical one. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility.

Social Choice and Welfare, 1984

Using axioms no stronger than those for the Neumann-Morgenstern expected utility hypothesis, with the recognition of finite sensibility, it is shown that the utility function derived by the N-M method is a neoclassical subjective utility function, contrary to the belief otherwise by prominent economists. This result is relevant for issues of utility measurability, social choice, etc. since it is subjective utility that is relevant for social choice. The relevance of individual risk aversion to the form of social welfare functions and the rationality of "pure" risk aversion are also discussed.

Economic Theory, 1993

We provide necessary and sufficient conditions for weak (semi)continuity of the expected utility. Such conditions are also given for the weak compactness of the domain of the expected utility. Our results have useful applications in cooperative solution concepts in economies and games with differential information, in noncooperative games with differential information and in principal-agent problems. I Introduction Recent work on cooperative solution concepts in economies and games with differential information (e.g. Yannelis [25,1, Krasa-Yannelis 1-16-1, Allen [2,3,1, Koutsougeras-Yannelis [17], Page [22]) has necessitated the consideration of conditions that guarantee the (semi)continuity of an agent's expected utility.1 Specifically, in this paper (g2, ~, P) is a probability space, representing the states of the world and their governing distribution, (V, I1" 11) a separable Banach space of commodities, and X :,(2 ~ 2 v a set-valued function, prescribing for each state ~o of the world the set X(~o) of possible consumptions. We define the set L~a~ of feasible state contingent consumption plans to consist of all Bochner integrable a.e. selections of X, that is, the set of all x~&~ such that x(~o)~X(og) a.e. in .(2. As usual, 5e~, stands for the (prequotient) set of all Bochner-integrable V-valued functions on (s ~, P); the ~ 1-seminorm on this space is defined by LIx tll:= LIx(,.

Annals of Operations Research, 1989

Some duality problems in expected utility theory, raised by the introduction of non-additive probabilities, are examined. Characterization of the probability measures, for which these problems do not arise, leads to an argument in favor of addivity.

We study the problem of obtaining an expected utility representation for a potentially incomplete preference relation over lotteries by means of a set of von Neumann-Morgenstern utility functions. It is shown that, when the prize space is a compact metric space, a preference relation admits such a multi-utility representation provided that it satisfies the standard axioms of expected utility theory. Moreover, the representing set of utilities is unique in a well-defined sense. r

Mind & Society, 2005