On the Fair and Efficient Allocation of Indivisible Commodities
On the Fair and Efficient Allocation of Indivisible Commodities

Author: Richard Engelbrecht-Wiggans

Publisher:

Published: 1978

Total Pages: 280

ISBN-13:

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Auctions and fair division problems are situations in which commodities are to be allocated fairly and efficiently. While a variety of schemes exist for fairly allocating finely divisible homogeneous commodities, most schemes are not applicable to the problem of allocating indivisible items. This paper considers the problem of fairly allocation sets of indivisible objects. 'Dollars, ' a finely divisible, homogeneous, transferrable commodity, are used to evaluate individuals preferences and to transfer value among individuals. This introduction of dollars has several implications; the main result is that fair allocation problems may be viewed as two smaller problems. First auction the goods among the individuals and then divide the resulting revenue according to the chosen definition of fairness. Several existing fair allocation schemes are reviewed; examples illustrate some difficulties associated with their use. Kuhn's definitions of 'fairness' are presented and two extensions are considered for the case where individuals have different shares in the collection of goods.

Efficiency and Fairness in the Allocation of Indivisible Goods
Efficiency and Fairness in the Allocation of Indivisible Goods

Author: Akina Ikudo

Publisher:

Published: 2021

Total Pages: 147

ISBN-13:

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This dissertation studies the efficient and fair allocation of indivisible goods without monetary transfer. It is a collection of three papers and uses school-choice programs as a motivating example. I provide theoretical results that can guide the design of new allocation systems as well as tools that can be used to enhance existing systems. In Chapter 1, I analyze how information disclosure affects social welfare using a stylized model. In my model, the utility of agents consists of a vertical "quality" component and a horizontal "idiosyncratic taste" component. The exact qualities of the objects are unknown to the agents, and the social planner seeks an information-disclosure policy that will maximize the total utility. The results show that (1) the optimal disclosure policy hides small differences in quality and reveals large differences in quality, (2) more information is disclosed when the valuations of the quality are heterogeneous, and (3) the Immediate Acceptance mechanism is more conducive for information disclosure than the Deferred Acceptance mechanism. In Chapter 2, I study the collocation of groups of students in school-choice programs. In particular, I examine when and how stochastic assignment matrices can be decomposed into lotteries over deterministic assignments subject to collocation constraints. I first show that---regardless of the number of pairs of twins in the student body---twin collocation can be maintained in a decomposition if one extra seat can be added to each school. I then propose a decomposition algorithm based on Column Generation that can incorporate a wide variety of constraints including collocation constraints. In Chapter 3, I propose a new notion of fairness that combines the concept of rank values and the maximin principle. An assignment is rank-egalitarian undominated (REU) if there is no other assignment that is equally or more egalitarian for any set of rank values. I show that each REU assignment can be generated as a solution to a linear programming problem that maximizes the weighted sum of expected rank values of the worst-off agents. I also provide an algorithm that generates special subsets of REU assignments that are practically important.

Fair Division and Collective Welfare
Fair Division and Collective Welfare

Author: Herve Moulin

Publisher: MIT Press

Published: 2004-08-20

Total Pages: 302

ISBN-13: 9780262633116

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The concept of fair division is as old as civil society itself. Aristotle's "equal treatment of equals" was the first step toward a formal definition of distributive fairness. The concept of collective welfare, more than two centuries old, is a pillar of modern economic analysis. Reflecting fifty years of research, this book examines the contribution of modern microeconomic thinking to distributive justice. Taking the modern axiomatic approach, it compares normative arguments of distributive justice and their relation to efficiency and collective welfare. The book begins with the epistemological status of the axiomatic approach and the four classic principles of distributive justice: compensation, reward, exogenous rights, and fitness. It then presents the simple ideas of equal gains, equal losses, and proportional gains and losses. The book discusses three cardinal interpretations of collective welfare: Bentham's "utilitarian" proposal to maximize the sum of individual utilities, the Nash product, and the egalitarian leximin ordering. It also discusses the two main ordinal definitions of collective welfare: the majority relation and the Borda scoring method. The Shapley value is the single most important contribution of game theory to distributive justice. A formula to divide jointly produced costs or benefits fairly, it is especially useful when the pattern of externalities renders useless the simple ideas of equality and proportionality. The book ends with two versatile methods for dividing commodities efficiently and fairly when only ordinal preferences matter: competitive equilibrium with equal incomes and egalitarian equivalence. The book contains a wealth of empirical examples and exercises.

Handbook of Social Choice and Welfare
Handbook of Social Choice and Welfare

Author: Kenneth J. Arrow

Publisher: Elsevier

Published: 2010-10-13

Total Pages: 985

ISBN-13: 0080929826

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This second part of a two-volume set continues to describe economists' efforts to quantify the social decisions people necessarily make and the philosophies that those choices define. Contributors draw on lessons from philosophy, history, and other disciplines, but they ultimately use editor Kenneth Arrow's seminal work on social choice as a jumping-off point for discussing ways to incentivize, punish, and distribute goods. - Develops many subjects from Volume 1 (2002) while introducing new themes in welfare economics and social choice theory - Features four sections: Foundations, Developments of the Basic Arrovian Schemes, Fairness and Rights, and Voting and Manipulation - Appeals to readers who seek introductions to writings on human well-being and collective decision-making - Presents a spectrum of material, from initial insights and basic functions to important variations on basic schemes

A Theory of Fairness and Social Welfare
A Theory of Fairness and Social Welfare

Author: Marc Fleurbaey

Publisher: Cambridge University Press

Published: 2011-06-13

Total Pages: 315

ISBN-13: 1139498770

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The definition and measurement of social welfare have been a vexed issue for the past century. This book makes a constructive, easily applicable proposal and suggests how to evaluate the economic situation of a society in a way that gives priority to the worse-off and that respects each individual's preferences over his or her own consumption, work, leisure and so on. This approach resonates with the current concern to go 'beyond the GDP' in the measurement of social progress. Compared to technical studies in welfare economics, this book emphasizes constructive results rather than paradoxes and impossibilities, and shows how one can start from basic principles of efficiency and fairness and end up with concrete evaluations of policies. Compared to more philosophical treatments of social justice, this book is more precise about the definition of social welfare and reaches conclusions about concrete policies and institutions only after a rigorous derivation from clearly stated principles.

Stability and Perfection of Nash Equilibria
Stability and Perfection of Nash Equilibria

Author: Eric van Damme

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 331

ISBN-13: 364296978X

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The last decade has seen a steady increase in the application of concepts from noncooperative game theory to such diverse fields as economics, political science, law, operations research, biology and social psychology. As a byproduct of this increased activity, there has been a growing awareness of the fact that the basic noncooperative solution concept, that of Nash equilibrium, suffers from severe drawbacks. The two main shortcomings of this concept are the following: (i) In extensive form games, a Nash strategy may prescribe off the equilibrium path behavior that is manifestly irrational. (Specifically, Nash equilibria may involve incredible threats), (ii) Nash equilibria need not be robust with respect to small perturbations in the data of the game. Confronted with the growing evidence to the detriment of the Nash concept, game theorists were prompted to search for more refined equilibrium notions with better properties and they have come up with a wide array of alternative solution concepts. This book surveys the most important refinements that have been introduced. Its objectives are fourfold (i) to illustrate desirable properties as well as drawbacks of the various equilibrium notions by means of simple specific examples, (ii) to study the relationships between the various refinements, (iii) to derive simplifying characterizations, and (iv) to discuss the plausibility of the assumptions underlying the concepts.