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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.

The original publication is available at www.springerlink.com We consider a model of political competition among two ideological parties who are uncertain about the distribution of voters. The distinguishing feature of the model is that parties can delegate electoral decisions to candidates by nomination. It is shown that if the credible platform commitments of the candidates is feasible, then at least one of the parties nominates in equilibrium to a candidate who has an ideology that is more radical than the delegating party’s ideology. In a variety of circumstances, this, in turn, yields a polarization of equilibrium policy choices of the candidates. It is thus argued formally here that strategic nomination of the candidates may well be one of the major reasons behind the well documented observation that the platforms associated with the political parties in two-party democracies are often surprisingly polarized. We gratefully acknowledge the financial support from the Spanish Ministry of Education through grant CICYT BEC2001-0535 (Faulí-Oller) and BEC2001-0980 (Ortuño-Ortín) Publicado

Many strategic interactions in the real world take place among delegates empowered to act on behalf of others. Managers make strategic decisions that affect profits; sales persons have power over setting prices; and lawyers and sports agents represent their clients in bargaining processes. One of the central messages of game theory is that this could be, at least partly, due to the strategic advantage delegation may provide to the delegating party. The idea that signing binding and publicly observable contracts with a third party may serve as a beneficial commitment device goes back at least to Schelling (1960), and has been put into use in many areas of economics.1 However, the observability of contracts appears to be a precondition for them to play a commitment role, and for this reason, almost all applications of strategic delegation theory are couched in terms of observable contracts. The formalization of this intuition is given by Katz (1991) who showed that if contracts are unobservable, then the Nash equilibrium outcomes of a game with and without delegation coincide. In particular, delegation through unobservable contracts does not change the predicted outcome of games with a unique Nash equilibrium. These observations, in turn, call the empirical relevance of the applied delegation studies into serious question since, in most real-world transactions, the signed contracts are unobservable to the outside parties. However, there are important strategic environments that fall outside the confines of Katz's analysis. First, Katz's model does not include the scenarios in which the outcome of the decision of delegating or not delegating is observable to the outside party. In contrast, in some models it is natural that the outside party observes the outcome of this decision simply because (s)he

Interest in economic mobility stems largely from its perceived role as an equalizer of opportunities, though not necessarily of outcomes. In this paper we show that this view leads very naturally to a methodology for the measurement of social mobility which has strong parallels with the theory of progressive taxation. We characterize opportunity--equalizing mobility processes, and provide simple criteria to determine when one process is more equalizing than another. We then explain how this mobility ordering relates to social welfare analysis, and how it differs from existing ones. We also extend standard indices of tax progressivity to mobility processes, and illustrate our general methodology on intra- and intergenerational mobility data from the United States and Italy.

We consider two-person bargaining games with interdependent preferences and bilateral incomplete information. We show that in both the ultimatum game and the two-stage alternating-offers game, our equilibrium predictions are consistent with a number of robust experimental regularities that falsify the standard game-theoretic model: occurrence of disagreements, disadvantageous counteroffers, and outcomes that come close to the equal split of the pie. In the context of infinitehorizon bargaining, the implications of the model pertaining to fair outcomes are even stronger. In particular, the Coase property in our case generates “almost” 50-50 splits of the pie, almost immediately. The present approach thus provides a positive theory for the frequently encountered phenomenon of the 50-50 division of the gains from trade.

Evaluation of distributions of income on the basis of equality is one of the most extensively studied topics in the general field of welfare economics. There is thus an enormous body of work devoted exclusively to the problem of the measurement of welfare and income inequality experienced by a given society.2 However, the majority of these studies are conducted in static terms, where the so-called “snapshots” of the income distributions are taken as the primitives of the analysis. Nevertheless, static evaluations of income distributions can provide only an incomplete picture, for, in most instances, the social welfare would certainly depend on the dynamics of income distribution as well.3 This basic insight, along with the increased availability of longitudinal data sets, has led to a massive and rapidly expanding literature on the measurement of income mobility. This chapter surveys the highlights of this literature.

We consider the problem of ranking distributions of opportunity sets on the basis of equality. First, conditional on a given ranking of individual opportunity sets, we define the notion of an equalizing transformation. Then, assuming that the opportunity sets are ranked according to the cardinality ordering, we formulate the analogues of the notions of the Lorenz partial ordering, equalizing (Dalton) transfers, and inequality averse social welfare functions – concepts which play a central role in the literature on income inequality. Our main result is a cardinality-based 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 rank preserving equalizations, and if and only if the former is ranked higher than the latter by all inequality averse social welfare functions. In addition, we characterize the smallest monotonic and transitive extension of our cardinality-based Lorenz inequality ordering.

We study the evolution of preference interdependence in aggregative games which are symmetric with respect to material payoffs but asymmetric with respect to player objective functions. We identify a class of aggregative games whose equilibria have the property that the players with interdependent preferences (who care not only about their own material payoffs but also about their payoffs relative to others) earn strictly higher material payoffs than do the material payoff maximizers. Implications of this finding for the theory of preference evolution are discussed. Journal of Economic Literature Classification Numbers: C72, D62.

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.

We develop a theory of representation of interdependent preferences that reflect the widely acknowledged phenomenon of keeping up with the Joneses (i.e. of those preferences which maintain that well-being depend on "relative standing" in the society as well as on material consumption). The principal ingredient of our analysis is the assumption that individuals desire to occupy a (subjectively) better position than their peers. This is quite a primitive starting point in that it does not give any reference to what is actually regarded as "status" in the society. We call this basic postulate negative interdependence, and study its implications. In particular, combining this assumption with some other basic postulates that are widely used in a number of other branches of the theory of individual choice, we axiomatize the relative income hypothesis, and obtain an operational representation of interdependent preferences.

This paper studies the possibility of progressive income taxation of heterogeneous populations. While a result due to Moyes and Shorrocks (1994) indicates that there does not exist a universally inequality-reducing tax structure which distinguishes between at least two subpopulations (in the sense of applying a different tax function to each subclass), it is shown here that a minimal refinement of the universality of inequality reduction leads one to a possibility conclusion. Informally stated, we prove the existence of uncountably many differentiated tax structures which are strictly progressive almost everywhere.

The typical practice of income inequality evaluation is by using inequality indices. Yet there is no “best” measure of inequality as we know it, and hence, any conclusion based on an inequality index must be subject to some doubts. Some authors even argued that the concept of inequality, by its very nature, is vague, and thus, cannot be measured like an exact concept. Motivated by these considerations, this paper studies axiomatic fuzzifications of inequality measures. Consequently, a systematic method of viewing the conclusions of inequality comparisons in terms of truth value statements is developed. Furthermore, it is shown that this method (or in fact, any other fuzzy inequality measure) can be used to construct confidence intervals for the crisp conclusions of inequality indices.

This paper shows that, in the domain of piecewise linear statutory income tax functions, the principle of equal sacrifice implies tax progressivity. The progressivity implication of the doctrine is, in fact, stronger: the equal sacrifice principle, in essence, characterizes marginal rate progressivity, a result which is in sharp contrast with the standard literature on public finance. The authors also apply their findings to the personal statutory income taxation practices of the OECD countries and observe that the United States and Turkey were the only ones violating the principle of equal sacrifice in the time period 1988 to 1991. Copyright 1996 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

We study the existence of maximum and minimum solutions to generalized variational inequalities on Banach lattices. The main tools of analysis are the variational characterization of the generalized metric projection operator and order-theoretic fixed point theory.

A graduate level introduction to probability theory designed for graduate students in economics.