Utility Representation of an Incomplete Preference Relation

We consider the problem of representing a (possibly) incomplete preference relation by means of a vector-valued utility function. Continuous and semicontinuous representation results are reported in the case of preference relations that are, in a sense, not “too incomplete.” These results generalize some of the classical utility representation theorems of the theory of individual choice and paves the way towards developing a consumer theory that realistically allows individuals to exhibit some “indecisiveness” on occasion. Journal of Economic Literature Classification Number: D11.     

A Revealed Preference Theory for Non-expected Utility on "Certain × Uncertain" Consumption Pairs

In this paper we consider a two-period decision problem, where the feasible set is the set of "certain × uncertain" consumption pairs. That is, the decision-maker chooses ( x , m ) in a feasible set, where x is a certain first-period consumption and m is a random second-period consumption, a Borel probability measure on the set of real numbers. The purpose of this paper is to present revealed preference theory for non-expected utility on "certain × uncertain" consumption pairs. We present necessary and sufficient conditions for the data to be consistent with some non-expected utility functions.
JEL Classification Numbers: D11, D81, D91     

效用理论在保险中的应用

保险决策中的基本问题之一是确定保单、计算保费用效理论保单、计算保费，比绵方法更加精确、可靠。再保险在我国刚刚起步，用效用理论可以一种最优再保。     

Insurance Taxation and Insurance Fraud

It is common practice in the United States to impose a sales tax on insurance premiums. Insurance benefits are not taxed, and it is typically argued that they should not be taxed because they compensate for a loss. In this paper I present a case where the taxation of insurance benefits is preferable to the taxation of premiums. When insurance fraud is present—in the form of ex post moral hazard—a tax on insurance premiums increases the number of fraudulent claims in the economy, whereas a tax on insurance benefits may reduce fraud. More importantly, however, policyholders are made better off with a benefit tax than with a premium tax.     

Unforeseen Contingencies and Incomplete Contracts

We scrutinize the conceptual framework commonly used in the incomplete contract literature. This literature usually assumes that contractual incompleteness is due to the transaction costs of describing—or of even foreseeing—the possible states of nature in advance. We argue, however, that such transaction costs need not interfere with optimal contracting ( i.e. transaction costs need not be relevant ), provided that agents can probabilistically forecast their possible future payoffs (even if other aspects of the state of the nature cannot be forecast). In other words, all that is required for optimality is that agents be able to perform dynamic programming, an assumption always invoked by the incomplete contract literature. The foregoing optimality result holds very generally provided that parties can commit themselves not to renegotiate. Moreover, we point out that renegotiation may be hard to reconcile with a framework that otherwise presumes perfect rationality. However, even if renegotiation is allowed, the result still remains valid provided that parties are risk averse.     

Utility and entropy

Summary. In this paper we study an astonishing similarity between the utility representation problem in economics and the entropy representation problem in thermodynamics. Received: May 17, 1999; revised version: October 16, 2000     

Incomplete markets and individual risks

Summary This paper studies the incomplete markets model with financial assets when the only missing markets are for individual risks. There are no aggregate risks in the economy. Assuming the individual risks are only privately observable, the only equilibria that are implementable by anonymous mechanisms are those in which prices do not vary across states of the world. Such equilibria always exist. Generically, they are locally unique and depend continuously on the parameters of the economy, just like complete-markets equilibria. Generically, there is also an infinite-dimensional manifold of equilibria in which prices do vary across states of the world. These equilibria are isomorphic to sunspot equilibria.I am grateful to Dave Cass for several helpful discussions and to Darrell Duffie for his comments on an earlier draft.     

Mixed-Strategy Nash Equilibrium Based upon Expected Utility and Quadratic Utility

The notion of a mixed-strategy Nash equilibrium suffers from three inherent difficulties. First, given the equilibrium strategies of other players, there are many best replies. Second, the equilibrium is unstable. Third, comparative statics results are counterintuitive. We demonstrate that these difficulties all have their origin in von Neumann and Morgenstern′s expected utility. In contrast, players with "quadratic utility" have unique best replies and the Nash equilibrium appears to yield intuitive comparative statics results. Journal of Economic Literature Classification Number: C72.     

Incomplete insurance and absolute risk aversion

Suppose that a subset of states of nature are not verifiable individually. Given an optimal feasible insurance scheme, the expected utility across a group of unverifiable states is greater (less) than that of a verifiable state, if the degree of absolute risk aversion is decreasing (increasing).     

Incomplete financial markets and differential information

We provide a model of an incomplete markets economy where private restrictions on consumption are interpreted as lack of information. We prove existence of an equilibrium where agents are unable to infer any additional information from prices. When assets are nominal, these non-enlightening equilibrium prices result in a reduction of the degree of real indeterminacy.     

Self-Flagellation and Utility Maximization

Abstract

Economic models explain human behavior only to the degree that the underlying assumptions of the model are fulfilled. Consumer theory of rational choice has been applied to a wide array of situations. This paper examines the results of the model when a consumer considers bundles of goods, some of which may affect her self image. Under these conditions, wrong decisions are not easily corrected, but can more easily be reversed if the individual is able to forgive herself for having made the wrong decision.     

Foundations of Incomplete Contracts

In the last few years, a new area has emerged in economic theory, which goes under the heading of "incomplete contracting". However, almost since its inception, the theory has been under attack for its lack of rigorous foundations. In this paper, we evaluate some of the criticisms that have been made of the theory, in particular, those in Maskin and Tirole (1999 a ). In doing so, we develop a model that provides a rigorous foundation for the idea that contracts are incomplete.     

Incomplete preferences and rational intransitivity of choice

Do violations of classical rationality theory imply that agents are acting against their self-interest? To answer this question, we investigate whether completeness and transitivity necessarily hold when agents choose outcome rationally—that is, their choice sequences do not lead to dominated outcomes. We show that, because of the danger of money pumps and other manipulations, outcome rationality implies that agents must have transitive psychological preferences. Revealed preferences, on the other hand, must be complete since agents can be forced to choose from any set of options. But these justifications of transitivity and completeness cannot be combined. We show that if psychological preferences are incomplete then revealed preferences can be intransitive without exposing agents to manipulations or violating outcome rationality. We also show that a specific case of nonstandard behavior, status quo maintenance, is outcome-rational in the simple environments considered in the experimental literature, but not in more complex settings.     

Non-paternalistic Altruism and Utility Interdependence

This paper clarifies the notion of non-paternalistic altruism through the use of utility aggregators. It presents conditions for the existence of non-paternalistically altruistic utility functions and provides a complete characterization of such utility functions. The results are used to generalize the Second Theorem of Welfare Economics and to prove the existence of an equilibrium in a game of voluntary gift-giving.
JEL Classification Nos.: D11, D64.     

Incomplete information in rent-seeking contests

We consider a variant of the Tullock lottery contest. Each player’s constant marginal cost of effort is drawn from a potentially different continuous distribution. In order to study the impact of incomplete information, we compare three informational settings to each other; players are either completely informed, privately informed about their own costs, or ignorant of all cost realizations. For the first and the third setting, we determine the unique pure-strategy Nash equilibrium. Under private information, we prove existence of a pure-strategy Bayesian Nash equilibrium and identify a sufficient condition for uniqueness. Assuming that unit cost distributions all have the same mean, we show that under ignorance of all cost realizations ex ante expected aggregate effort is lower than under both private and complete information. Ex ante expected rent dissipation, however, is higher than in the latter settings if we focus on the standard lottery contest and assume costs are all drawn from the same distribution. Between complete and private information, there is neither a general ranking in terms of effort nor in terms of rent dissipation.     

Regional Insurance and Migration

A dynamic model of migration is developed to study whether labor mobility can hedge people against region-specific shocks, making private or public insurance redundant. The model adopts a novel timing for migration, which is argued to be the time frame suitable for analyzing risk-sharing issues. It also innovates on the existing literature by solving individual migration through convexification of the set of actions. The results show that the role of migration as an insurance mechanism is small: labor mobility cannot fully remove income differentials between regions. It is also shown that a fiscal stabilization scheme is, in general, optimal; moreover, any pure risk-sharing mechanism has no influence on migration flows.     

Insurance monopoly and renegotiation

Summary The mechanism design problem of a monopoly insurer — faced with privately informed insurees — is considered. It is assumed that the insurer cannot commit not to renegotiate (by using the information that customer separation reveals) before contracts are put into force. A solution is offered by modeling renegotiation-proofness in a framework inspired by Greenberg's theory of social situations. Maximizing profit within the set of renegotiation-proof outcomes always leads to a semi-separating outcome (i.e. neither full pooling nor full separation can occur) and may leave all low-risks as well as some of the high-risks self-insured.This work originated with Asheim and Nilssen (1991). The authors thank Paul Beaudry, Mathias Dewatripont, John Hillas, Terje Lensberg, Georg Nöldeke, Trond Olsen, Michel Poitevin, Eric van Damme, and especially Joseph Greenberg, as well as participants at seminars in Bergen, Cambridge, Florence, Helsinki, London, Mons, Montreal, Oslo, Stony Brook, and Tilburg for helpful comments and discussions. Asheim thanks Tilburg (CentER), McGill and Humboldt Universities for their hospitality and acknowledges support from the Norwegian Research Centre in Organization and Management and the Norwegian Research Council. Nilssen acknowledges support from Norges Bank and the Norwegian Research Council for Science and the Humanities.     

Insurance and Giffen's paradox

The letter gives a brief account of how insurance appears as an inferior good in standard economic analysis. It is argued that this result is due to unrealistic assumptions about how insurance premiums are calculated.