Aumann-Shapley Pricing : A Reconsideration of the Discrete Case

We reconsider the following cost-sharing problem: agent i = 1,...,n demands a quantity xi of good i; the corresponding total cost C(x1,...,xn) must be shared among the n agents. The Aumann-Shapley prices (p1,...,pn) are given by the Shapley value of the game where each unit of each good is regarded as a distinct player. The Aumann-Shapley cost-sharing method assigns the cost share pixi to agent i. When goods come in indivisible units, we show that this method is characterized by the two standard axioms of Additivity and Dummy, and the property of No Merging or Splitting: agents never find it profitable to split or merge their demands.

The Possibility of Ordering Infinite Utility Streams

This paper revisits Diamond’s classical impossibility result regarding the ordering of infinite utility streams. We show that if no representability condition is imposed, there do exist strongly Paretian and finitely anonymous orderings of intertemporal utility streams with attractive additional properties. We extend a possibility theorem due to Svensson to a characterization theorem and we provide characterizations of all strongly Paretian and finitely anonymous rankings satisfying the strict transfer principle. In addition, infinite horizon extensions of leximin and of utilitarianism are characterized by adding an equity preference axiom and finite translation-scale measurability, respectively, to strong Pareto and finite anonymity.

Relative Uncertainty and Additively Representable Set Rankings

This paper proposes a definition of relative uncertainty aversion for decision models under complete uncertainty. It is shown that, for a large class of decision rules characterized by a set of plausible axioms, the new criterion yields a complete ranking of those rules with respect to the relative degree of uncertainty aversion they represent. In addition, we address a combinatorial question that arises in this context, and we examine conditions for the additive representability of our rules.

Nearly Serial Sharing Methods

A group of agents participate in a cooperative enterprise producing a single good. Each participant contributes a particular type of input; output is nondecreasing in these contributions. How should it be shared? We analyze the implications of the axiom of Group Monotonicity: if a group of agents simultaneously decrease their input contributions, not all of them should receive a higher share of output. We show that in combination with other more familiar axioms, this condition pins down a very small class of methods, which we dub nearly serial.

Intertemporal Social Evaluation

Intertemporal social-evaluation rules provide us with social criteria that can be used to assess the relative desirability of utility distributions across generations. The trade-offs between the well-being of different generations implicit in each such rule reflect the underlying ethical position on issues of intergenerational equity or justice. We employ an axiomatic approach in order to identify ethically attractive socialevaluation procedures. In particular, we explore the possibilities of using welfare information and non-welfare information in a model of intertemporal social evaluation. We focus on the individuals’ birth dates and lengths of life as the relevant non-welfare information. As usual, welfare information is given by lifetime utilities. It is assumed that this information is available for each alternative to be ranked. Various weakenings of the Pareto principle are employed in order to allow birth dates or lengths of life (or both) to matter in social evaluation. In addition, we impose standard properties such as continuity and anonymity and we examine the consequences of an intertemporal independence property. For each of the Pareto conditions employed, we characterize all social-evaluation rules satisfying it and our other axioms. The resulting rules are birth-date dependent or lifetime-dependent versions of generalized utilitarianism. Furthermore, we discuss the ethical and axiomatic foundations of geometric discounting in the context of our model.

Consistent House Allocation

In practice we often face the problem of assigning indivisible objects (e.g., schools, housing, jobs, offices) to agents (e.g., students, homeless, workers, professors) when monetary compensations are not possible. We show that a rule that satisfies consistency, strategy-proofness, and efficiency must be an efficient generalized priority rule; i.e. it must adapt to an acyclic priority structure, except -maybe- for up to three agents in each object's priority ordering.

Rational Choice on Arbitrary Domains: A Comprehensive Treatment

The rationalizability of a choice function on arbitrary domains by means of a transitive relation has been analyzed thoroughly in the literature. Moreover, characterizations of various versions of consistent rationalizability have appeared in recent contributions. However, not much seems to be known when the coherence property of quasi-transitivity or that of P-acyclicity is imposed on a rationalization. The purpose of this paper is to fill this significant gap. We provide characterizations of all forms of rationalizability involving quasi-transitive or P-acyclical rationalizations on arbitrary domains.

Choosing Wisely: The Natural Multi-Bidding Mechanism

Pérez-Castrillo and Wettstein (2002) propose a multi-bidding mechanism to determine a winner from a set of possible projects. The winning project is implemented and its surplus is shared among the agents. In the multi-bidding mechanism each agent announces a vector of bids, one for each possible project, that are constrained to sum up to zero. In addition, each agent chooses a favorite a object which is used as a tie-breaker if several projects receive the same highest aggregate bid. Since more desirable projects receive larger bids, it is natural to consider the multi-bidding mechanism without the announcement of favorite projects. We show that the merits of the multi-bidding mechanism appear not to be robust to this natural simplification. Specifically, a Nash equilibrium exists if and only if there are at least two individually optimal projects and all individually optimal projects are efficient.

On Limits to the Use of Linear Markov Strategies in Common Property Natural Resource Games

We derive conditions that must be satisfied by the primitives of the problem in order for an equilibrium in linear Markov strategies to exist in some common property natural resource differential games. These conditions impose restrictions on the admissible form of the natural growth function, given a benefit function, or on the admissible form of the benefit function, given a natural growth function.

Domain Closedness Conditions and Rational Choice

The rationalizability of a choice function on an arbitrary domain under various coherence properties has received a considerable amount of attention both in the long-established and in the recent literature. Because domain closedness conditions play an important role in much of rational choice theory, we examine the consequences of these requirements on the logical relationships among different versions of rationalizability. It turns out that closedness under intersection does not lead to any results differing from those obtained on arbitrary domains. In contrast, closedness under union allows us to prove an additional implication.

Social Choice: Recent Developments

In the past quarter century, there has been a dramatic shift of focus in social choice theory, with structured sets of alternatives and restricted domains of the sort encountered in economic problems coming to the fore. This article provides an overview of some of the recent contributions to four topics in normative social choice theory in which economic modelling has played a prominent role: Arrovian social choice theory on economic domains, variable-population social choice, strategy-proof social choice, and axiomatic models of resource allocation.

The Dynamic (In)efficiency of Monetary Policy by Committee

This paper develops a model where the value of the monetary policy instrument is selected by a heterogenous committee engaged in a dynamic voting game. Committee members differ in their institutional power and, in certain states of nature, they also differ in their preferred instrument value. Preference heterogeneity and concern for the future interact to generate decisions that are dynamically ineffcient and inertial around the previously-agreed instrument value. This model endogenously generates autocorrelation in the policy variable and provides an explanation for the empirical observation that the nominal interest rate under the central bank’s control is infrequently adjusted.

Consistent Relations

Consistency, a natural weakening of transitivity introduced in a seminal contribution by Suzumura (1976b), has turned out to be an interesting and promising concept in a variety of areas within economic theory. This paper summarizes its recent applications and provides some new observations in welfarist social choice and in population ethics. In particular, it is shown that the conclusion of the welfarism theorem remains true if transitivity is replaced by consistency and that an impossibility result in variable-population social-choice theory turns into a possibility if transitivity is weakened to consistency.

Solidarity in Choosing a Location on a Cycle

We study the implications of two solidarity conditions on the efficient location of a public good on a cycle, when agents have single-peaked, symmetric preferences. Both conditions require that when circumstances change, the agents not responsible for the change should all be affected in the same direction: either they all gain or they all loose. The first condition, population-monotonicity, applies to arrival or departure of one agent. The second, replacement-domination, applies to changes in the preferences of one agent. Unfortunately, no Pareto-efficient solution satisfies any of these properties. However, if agents’ preferred points are restricted to the vertices of a small regular polygon inscribed in the circle, solutions exist. We characterize them as a class of efficient priority rules.