The measurement of opportunity inequality: a cardinality-based approach

We consider the problem of ranking distributions of opportunity sets on the basis of equality. First, conditional on agents' preferences over individual opportunity sets, we formulate the analogues ofthe notions ofthe Lorenz partial ordering, equalizing Dalton transfers, and inequality averse social welfare functionals -concepts which play a central role in the literature on income inequality. For the particular case in which agents rank opportunity sets on the basis of their cardinalities, we establish an analogue of the fundamental theorem of inequality measurement: one distribution Lorenz dominates another if and only if the former can be obtained from the latter by a finite sequence of equalizing transfers, and if and only if the former is ranked higher than the latter by all inequality averse social welfare functionals. In addition, we characterize the smallest monotonic and transitive extension of the cardinality-based Lorenz inequality ordering

The measurement of opportunity inequality: a cardinality-based approach.

We consider the problem of ranking distributions of opportunity sets on the basis of equality. First, conditional on agents' preferences over individual opportunity sets, we formulate the analogues ofthe notions ofthe Lorenz partial ordering, equalizing Dalton transfers, and inequality averse social welfare functionals -concepts which play a central role in the literature on income inequality. For the particular case in which agents rank opportunity sets on the basis of their cardinalities, we establish an analogue of the fundamental theorem of inequality measurement: one distribution Lorenz dominates another if and only if the former can be obtained from the latter by a finite sequence of equalizing transfers, and if and only if the former is ranked higher than the latter by all inequality averse social welfare functionals. In addition, we characterize the smallest monotonic and transitive extension of the cardinality-based Lorenz inequality ordering.Opportunity Inequality; Equalizing Transfers; Lorenz Domination;

Delay aversion

We address the following question: When can one person properly be said to be more delay averse than another? In reply, several (nested) comparison methods are developed. These methods yield a theory of delay aversion which parallels that of risk aversion. The applied strength of this theory is demonstrated in a variety of dynamic economic settings, including the classical optimal growth and tree cutting problems, repeated games, and bargaining. Both time-consistent and time-inconsistent scenarios are considered.Delay aversion, impatience, consumption smoothing, time consistency

Real Analysis with Economic Applications

There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students. The emphasis throughout is on topics directly relevant to economic theory. In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. Efe Ok complements the mathematical development with applications that provide concise introductions to various topics from economic theory, including individual decision theory and games, welfare economics, information theory, general equilibrium and finance, and intertemporal economics. Moreover, apart from direct applications to economic theory, his book includes numerous fixed point theorems and applications to functional equations and optimization theory. The book is rigorous, but accessible to those who are relatively new to the ways of real analysis. The formal exposition is accompanied by discussions that describe the basic ideas in relatively heuristic terms, and by more than 1,000 exercises of varying difficulty. This book will be an indispensable resource in courses on mathematics for economists and as a reference for graduate students working on economic theory.real analysis, economic applications, order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, calculus of variations

On the Strategic Advantage of Negatively Interdependent Preferences

We study certain classes of supermodular and submodular games which are symmetric with respect to material payoffs but in which not all players seek to maximize their material payoffs. Specifically, a subset of players have negatively interdependent preferences and care not only about their own material payoffs but also about their payoffs relative to others. We identify sufficient conditions under which members of the latter group have a strategic advantage in the following sense: at all intragroup symmetric equilibria of the game, they earn strictly higher material payoffs than do players who seek to maximize their material payoffs. We show that these conditions are satisfied by a number of games of economic importance, and discuss the implications of these findings for the evolutionary theory of preference formation and the theory of Cournot competition.Interdependent Preferences, Submodular and Supermodular Games, Relative Profits, Cournot Oligopoly

Expected Utility Theory without the Completeness Axiom

We study axiomatically 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.Expected utility, incomplete preferences

Interdependent Preference Formation

A standard assumption in the economic approach to individual decision making is that people have independent preferences, that is, they care only about their absolute (material) payoffs. We study equilibria of the classic common pool resource extraction and public good games when some of the players have negatively interdependent preferences (in the sense that they care not only about their absolute payoffs but also about their relative payoffs) while the remainder have independent preferences. It is shown that at any equilibrium, those with interdependent preferences earn strictly higher absolute payoffs than do players with independent preferences. If the population composition evolves in accordance with any payoff monotonic evolutionary selection dynamics, then all players will have interdependent preferences in the long run. Similar (but weaker) results obtain for some other economically important classes of games in strategic form. The robustness of our findings with respect to other preference formation mechanisms such as myopic and rational socialization is also discussed.Interdependent Preferences, Evolution, Socialization.

Stochastic Dominance in Mobility Analysis

This paper introduces a technique for mobility dominance and compares the degree of earnings mobility of men in the USA from 1970 to 1995. The highest mobility is found in the 1975–1980 or 1980–1985 periods