Von Neumann–Morgenstern utility theorem

About: Von Neumann–Morgenstern utility theorem is a research topic. Over the lifetime, 1187 publications have been published within this topic receiving 100005 citations.

Prospect theory: an analysis of decision under risk

Abstract: This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low prob- abilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling. EXPECTED UTILITY THEORY has dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice (24), and widely applied as a descriptive model of economic behavior, e.g. (15, 4). Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory (47, 36), and that most people actually do, most of the time. The present paper describes several classes of choice problems in which preferences systematically violate the axioms of expected utility theory. In the light of these observations we argue that utility theory, as it is commonly interpreted and applied, is not an adequate descriptive model and we propose an alternative account of choice under risk. 2. CRITIQUE

A theory of anticipated utility

Abstract: A new theory of cardinal utility, with an associated set of axioms, is presented. It is a generalization of the von Neumann-Morgenstern expected utility theory, which permits the analysis of phenomena associated with the distortion of subjective probability.

Subjective probability and expected utility without additivity

Abstract: An act maps states of nature to outcomes; deterministic outcomes as well as random outcomes are included. Two acts f and g are comonotonic, by definition, if it never happens that f(s) >- f(t) and g(t) >- g(s) for some states of nature s and t. An axiom of comonotonic independence is introduced here. It weakens the von Neumann-Morgenstern axiom of independence as follows: If f >- g and if f, g, and h are comonotonic, then cff +(l-a)h>-ag+(1 -ac)h. If a nondegenerate, continuous, and monotonic (state independent) weak order over acts satisfies comonotonic independence, then it induces a unique non-(necessarily-)additive probability and a von Neumann-Morgenstern utility. Furthermore, one can compute the expected utility of an act with respect to the nonadditive probability, using the Choquet integral. This extension of the expected utility theory covers situations, as the Ellsberg paradox, which are inconsistent with additive expected utility. The concept of uncertainty aversion and interpretation of comonotonic independence in the context of social welfare functions are included.

Regret in Decision Making under Uncertainty

Abstract: Evidence exists that people do not always make decisions involving uncertain monetary rewards as if they were maximizing expected utility of final assets. Explanations for this behavior postulate that the cognitive demands of consistency to such a theory are too great. However, situations exist in which more than mental shortcuts are involved and these anomalies raise questions about expected utility theory as a guide to behavior. This paper explores the possibility that expected utility theory appears to fail because the single outcome descriptor—money—is not sufficient. After making a decision under uncertainty, a person may discover, on learning the relevant outcomes, that another alternative would have been preferable. This knowledge may impart a sense of loss, or regret. The decision maker who is prepared to tradeoff financial return in order to avoid regret will exhibit some of the behavioral paradoxes of decision theory. By explicitly incorporating regret, expected utility theory not only becomes a...

Utility theory for decision making

Abstract: : The book presents a concise yet mathematically complete treatment of modern utility theories that covers nonprobabilistic preference theory, the von Neumann-Morgenstern expected-utility theory and its extensions, and the joint axiomatization of utility and subjective probability.