Edi Karni

Risk aversion in the theory of expected utility with rank dependent probabilities

Expected utility with rank dependent probability theory is a model of decision-making under risk where the preference relations on the set of probability distributions is represented by the mathematical expectation of a utility function with respect to a transformation of the probability distributions on the set of outcomes. This paper defines, based on Gâteaux differentiability, measures of risk aversion for such preferences which characterize the relation “more risk averse” and applies these measures to the analysis of unconditional and conditional portfolio choice problems.

Utility theory with uncertainty

Publisher Summary Utility theory with uncertainty describes a class of models designed to formalize the manner in which a decision maker chooses among alternative courses of action when the consequences of each course of action are not known at the time the choice is made. The distinguishing characteristic of the subject matter is that each course of action results in one of several consequences. The chapter discusses that the problem is conveniently formalized with the use of the notions of consequences, states of nature, and acts. The first primitive of the theory is a nonempty set of consequences, denoted by C. The empirical counterpart of a consequence is anything that has to do with the welfare of the decision maker. The second primitive of the theory is a nonempty set of feasible acts, denoted by A 0 , whose elements are courses of action from which the decision maker may choose. Decision problems in which the set of states is a singleton, or in which all acts are constant acts, and the set of consequences consists of probability measures or lotteries on a set of outcomes are referred to as “decisions under risk;” if the set of acts includes nonconstant acts they are decisions under uncertainty. Given the primitives of the theory, a complete and transitive binary relation on the set of consequences is a natural ingredient necessary to guide the decision makers choices among acts. In the theory of choice under certainty, there is a one-to-one correspondence between acts and consequences.

Individual Sense of Justice: A Utility Representation

We present an axiomatic model depicting the choice behavior of a self-interest seeking moral individual over random allocation procedures. Individual preferences are decomposed into a self-interest component and a component representing the individuals moral value judgment. Each component has a distinct utility representation, and the preference relation depicting the choice behavior is representable by a real-valued function defined on the components utilities. The utility representing the self-interest component is linear and the utility representing the individuals moral value judgment is quasi-concave. The addition of a hexagon condition implies that the utility representing the individuals preference is additively separable in the components utilities.

On the conjunction fallacy in probability judgment: New experimental evidence regarding Linda

This paper reports the results of a series of experiments designed to test whether and to what extent individuals succumb to the conjunction fallacy. Using an experimental design of Tversky and Kahneman (1983), it finds that given mild incentives, the proportion of individuals who violate the conjunction principle is significantly lower than that reported by Kahneman and Tversky. Moreover, when subjects are allowed to consult with other subjects, these proportions fall dramatically, particularly when the size of the group rises from two to three. These findings cast serious doubts about the importance and robustness of such violations for the understanding of real-life economic decisions.

Atemporal dynamic consistency and expected utility theory

Abstract In this paper we represent atemporal sequential decisions as compound lotteries. We show that a preference relation defined on the set of conditional lotteries (i.e., sublotteries conditioned on the lotteries to which they belong) that satisfies consequentialism and the axiom of reduction of compound lotteries, satisfies the independence axiom of expected utility theory if and only if it satisfies dynamic consistency.

Social Attributes and Strategic Equilibrium: A Restaurant Pricing Game

Using a game-theoretic approach, we examine possible equilibrium explanations of the often-observed phenomenon that two neighboring restaurants offering similar menus nevertheless experience vastly different demands. The essential aspect of this analysis is the presence of a consumption externality that makes the popularity itself a factor in the determination of the relative attractiveness of the restaurants.

SUBJECTIVE EXPECTED UTILITY WITH INCOMPLETE PREFERENCES

This paper extends the subjective expected utility model of decision making under uncertainty to include incomplete beliefs and tastes. The main results are two axiomatizations of the multiprior expected multiutility representations of preference relations under uncertainty. The paper also introduces new axiomatizations of Knightian uncertainty and the expected multiutility model with complete beliefs.

Optimal Unemployment Insurance: A Survey

Unemployment insurance improves the allocation of risk bearing at the cost of reduced incentives for work. In the past two decades, a branch of the literature has emerged that deals with the optimal design of unemployment insurance. This literature has been influenced by ideas and methods from information economics and by theories from labor economics. The result is a collection of models designed to highlight a variety of issues pertaining to the provision of optimal unemployment insurance. This paper reviews these issues, summarizes the relevant literature, assesses its accomplishments, and points out problems that require further study.

Dynamic Consistency, Revelations in Auctions and the Structure of Preferences

Power-driven warehouse equipment facilitates accurate and rapid selection of articles of commerce for distribution to warehouse outlets. A mobile track-mounted order-selection vehicle under the control of a warehouseman moves along an aisle formed by storage racks arranged in rows. Each rack is divided into compartments or slots, each slot containing cases, cartons or containers of a designated article of commerce. As the vehicle moves along the slots, selection of type and quantity of containers is made in accordance with a predetermined program carried by the driver of the vehicle in accordance with order picking instructions displayed for him by a display unit on the vehicle. Following selection of the requisite type and quantity of containers, each container is automatically labeled with a label which indicates the type, quantity and destination information imprinted thereon according to a program, and the containers are mechanically transported to an area where they are automatically diverted to accomplish assembly of orders in accordance with their proper destination.

Self-preservation as a foundation of rational behavior under risk

Abstract This paper derives an expected utility theorem from the principle of self-preservation thus providing a new interpretation of the notion of rationality underlying the von Neumann-Morgenstern theory. Self-preservation is defined as the maximization of the probability of survival in a finite horizon model where in each period the decision maker must choose a risky prospect from a feasible set of such prospects and becomes extinct if his accumulated fortune becomes non-positive. It is shown that the choice of the optimal strategy may be regarded as an expected utility maximizing behavior and that violations of the independence axiom, e.g., Allais paradox, imply that decision-makers choose a probability of survival smaller than the maximum possible given the set of acts. Furthermore, according to this approach rational attitudes toward risk are also derived from the model.