Efficiency and truthfulness with Leontief preferences. A note on two-agent,two-good economies

In exchange economies where agents have private information about their preferences, strategy-proof and individually rational social choice functions are in general not efficient. We provide a restricted domain, namely the set of preferences representable by Leontief utility functions, where there exist mechanisms which are strategy-proof, efficient and individually rational. In two-agent, two-good economies we are able to provide an even stronger result. We characterize the class of efficient and individually rational social choice functions, which are fully implementable in truthful strategies.Received: 28 April 2003, Accepted: 23 June 2003, JEL Classification: D51, D71The author thanks Matthew Jackson, Jordi Massó and James Schummer for fruitful discussions, William Thomson for many valuable comments on an earlier version. A particular thank to Salvador Barberá for his fundamental help.     

Strategy-proofness, core, and sequential trade

We extend the Shapley-Scarf (1974) model - where a finite number of indivisible objects is to be allocated among a finite number of individuals - to the case where the primary endowment set of an individual may contain none, one, or several objects and where property rights may be transferred (objects inherited) as the allocation process unfolds, under the retained assumption that an individual consumes at most one object. In this environment we analyze the core of the economy and characterize the set of strategy-proof and Pareto efficient mechanisms. As an alternative approach, we consider property rights implicitly defined by a strategy-proof and Pareto efficient mechanism and show a core property for the mechanism-induced endowment rule.Received: 19 February 2004, Accepted: 14 April 2005, JEL Classification: C71, C78, D71, D78We would like to thank two anonymous referees for valuable comments. Financial support from The Swedish Council for Research in the Humanities and Social Sciences is gratefully acknowledged by Lars-Gunnar Svensson. Financial support from The Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged by Bo Larsson.     

Design limits and dynamic policy analysis

This paper characterizes the frequency domain properties of feedback control rules in linear systems in order to better understand how different policies affect outcomes frequency by frequency. We are especially concerned in understanding how reductions of variance at some frequencies induce increases in variance at others. Tradeoffs of this type are known in the control literature as design limits. Design limits are important in understanding the full range of effects of macroeconomic stabilization policies. We extend existing results to account for discrete time bivariate systems with rational expectations. Application is made to the evaluation of monetary policy rules.     

The effects of age structure on economic growth: An application of probabilistic forecasting to India

During recent years there has been an increasing awareness of the explanatory power of population age structure variables in economic growth regressions. We estimate a new cross-country regression model of the effects of age structure change on economic growth. We use the new model and recent probabilistic demographic forecasts for India to derive the uncertainty of predicted economic growth rates caused by the uncertainty in demographic developments.     

Equivalence of optimal noisy-ranking contests and Tullock contests

We analyze a noisy-ranking contest in which participants compete in several dimensions. The organizer randomly samples a number of dimensions and awards a prize to the most productive agent. When the contest is optimally designed, we establish a structural equivalence between this family of noisy-ranking contests and contests built upon Tullock contest success functions. Our result also shows that in this class of noisy-contests, the profit-maximization problem of the planner can be turned into a stochastic choice problem for a planner who has some deterministic preferences over the contestants’ win probabilities.     

Probabilistic subjective expected utility

This paper develops the first model of probabilistic choice under subjective uncertainty (when probabilities of events are not objectively known). The model is characterized by seven standard axioms (probabilistic completeness, weak stochastic transitivity, nontriviality, event-wise dominance, probabilistic continuity, existence of an essential event, and probabilistic independence) as well as one new axiom. The model has an intuitive econometric interpretation as a Fechner model of (relative) random errors. The baseline model is extended from binary choice to decisions among m>2$m>2$ alternatives using a new method, which is also applicable to other models of binary choice.     

Games of chance with multiple objectives

We consider games of chance between two players: Player M can win only by amassing point totals in several categories before player N scores a prescribed total number n of points. Let M have k objectives, with m _i points required in category i and probability q _i of scoring a point in that category. We resolve certain special cases: (a) For all m _i equal, the probabilities of M winning are ordered by majorization of the vectors (q ₁,...,q _k ). (b) For all q _i equal, the probabilities of M winning are ordered by majorization of the vectors (m ₁,...,m _k ). (c) For all m _i equal and all q _i equal, the probability of M winning approaches 0 as n → ∞ or as k → ∞. The results, which follow from inequalities of majorization and Schur convexity, are in accord with intuition.      

Consistency in the probabilistic assignment model

This paper introduces a notion of consistency for the probabilistic assignment model, which we call probabilistic consistency. We show that the axioms equal treatment of equals and probabilistic consistency characterize the uniform rule, which is the rule which randomizes uniformly over all possible assignments.