Uzi Segal

First order versus second order risk aversion

This paper defines a new concept of attitude towards risk. For an actuarially fair random variable ϵ, π(t) is the risk premium the decisionmaker is willing to pay to avoid tϵ. In expected utility, and as it turns out, in the case of smooth Freechet differentiability of the representation functional, π′(0) = 0. There are models (e.g., rank dependent probabilities) in which ∂π∂t|t=0+ ≠ 0. We call the latter attitude as being of order 1, and we call the first one attitude of order 2. These concepts are then applied to analyze the problem of full insurance.

Two Stage Lotteries Without the Reduction Axiom

Preference relations over two-stage lotteries are analyzed. Empirical evidence indicates that decisionmakers do not always behave in accordance with the reduction of compound lotteries axiom, but they seem to satisfy a compound independence axiom. Although the reduction and the compound independence axioms, together with continuity, imply expected utility theory, each of them by itself is compatible with all possible preference relations over simple lotteries. Using these axioms, the author analyzes three different versions of expected utility for two-stage lotteries. The author suggests several different compound dominance axioms as possible replacements of the reduction axiom, which are strictly weaker than the reduction of compound lotteries axiom. Copyright 1990 by The Econometric Society.

Anticipated utility: a measure representation approach

This paper presents axioms which imply that a preference relation over lotteries can be represented by a measure of the area above the distribution function of each lottery. A special case of this family is the anticipated utility functional. One additional axiom implies this theory. This functional is then extended for the case of vectorial prizes.

MIXTURE SYMMETRY AND QUADRATIC UTILITY

The independence axiom of expected utility theory has recently been weakened to the betweenness axiom. In this paper, an even weaker axiom, called mixture symmetry, is presented. The corresponding functional structure is such that utility is a betweenness functional on part of this domain and quadratic in probabilities elsewhere. The experimental evidence against betweenness provides one motivation for the more general theory presented here. Another advantage of the mixture symmetric class of utility functions is that it is sufficiently flexible to permit the disentangling of attitudes toward risk and toward randomization. Copyright 1991 by The Econometric Society.

Tit for tat: Foundations of preferences for reciprocity in strategic settings

This paper assumes that in addition to the conventional (selfish) preferences over outcomes, players in a strategic environment have preferences over strategies. In the context of two-player games, it provides conditions under which a players preferences over strategies can be represented as a weighted average of the individuals selfish payoffs and the selfish payoffs of the opponent. The weight one player places on the opponents selfish utility depends on the opponents behavior. In this way, the framework is rich enough to describe the behavior of individuals who repay kindness with kindness and meanness with meanness. The paper assumes that each player has an ordering over his opponents strategies that describes the niceness of these strategies. It introduces a condition that insures that the weight on opponents utility increases if and only if the opponent chooses a nicer strategy.

Some remarks on Quiggin's anticipated utility

Abstract This remark proves that Quiggins anticipated utility function may solve the Allais paradox and the common ratio effect. For some generalizations of these it is needed to assume that the decision-weight function is concave.

Quadratic Social Welfare Functions

John Harsanyi has provided an intriguing argument that social welfare can be expressed as a weighted sum of individual utilities. His theorem has been criticized on the grounds that a central axiom, that social preference satisfies the independence axiom, has the morally unacceptable implication that the process of choice and considerations of ex ante fairness are of no importance. This paper presents a variation of Harsanyis theorem in which the axioms are compatible with a concern for ex ante fairness. The implied mathematical form for social welfare is a strictly quasi-concave and quadratic function of individual utilities.

Calibration Results for Non-Expected Utility Theories

Rabin proved that a low level of risk aversion with respect to small gambles leads to a high, and absurd, level of risk aversion with respect to large gambles. Rabins arguments strongly depend on expected utility theory, but we show that similar arguments apply to almost all non-expected utility theories.

Let's Agree That All Dictatorships Are Equally Bad

This paper shows that a minimal degree of consideration for other peoples well‐being enables society to agree that one social policy is the best. I offer axioms that imply that this best policy maximizes a weighted sum of individual utilities. The weight of each individual is the inverse of his or her maximal possible utility from social endowments. The suggested policy is not sensitive to the choice of the von Neumann‐Morgenstern utilities. The key axiom is that individuals agree that giving all the endowments always to one person is as bad as giving them to any other person.

Existence and dynamic consistency of Nash equilibrium with non-expected utility preferences☆

Sufficient conditions for the existence of a Nash equilibrium are given when preferences may violate the reduction of compound lotteries assumption (RCLA). Without RCLA decision makers may not be indifferent between compound lotteries which have the same probabilities of final outcomes. Therefore the conditions depend on how players perceive the game—whether they view themselves as moving first or second. We also review conditions under which the equilibria will be dynamically consistent.