The Geometry of Efficient Fair Division

Julius B. Barbanel

462 pages, parution le 07/04/2005

Ajouter à une liste

Indisponible

Résumé

What is the best way to divide a "cake" and allocate the pieces among some finite collection of players? In this book, the cake is a measure space, and each player uses a countably additive, non-atomic probability measure to evaluate the size of the pieces of cake, with different players generally using different measures. The author investigates efficiency properties (such as Pareto maximality: is there another partition that wouId make everyone at least as happy, and would make at least one player happier, than the present partition?) and fairness properties (such as envy - freeness: do all players think that their piece is at least as large as every other player's piece?). He focuses exclusively on abstract existence results rather than algorithms, and on the geometric objects that arise naturally in this context. By examining the shape of these objects and the relationship between them, he demonstrates results concerning the existence of efficient and fair partitions.

This is a work of mathematics that will be of interest to both mathematicians and economists.

L'auteur - Julius B. Barbanel

Julius B. Barbanel is Professor of Mathematics at Union College, where he has also served as Department Chair. He has published numerous articles in the areas of both Logic and Set Theory, and Fair Division in leading mathematical journals.

Sommaire

Preface
Notation and preliminaries
Geometric object #1a: the individual pieces set (IPS) for two players
What the IPS tells us about fairness and efficiency in the two-player context
The general case of n players
What the IPS and the FIPS tell us about fairness and efficiency in the n-player context
Characterizing Pareto optimality: introduction and preliminary ideas
Characterizing Pareto optimality I: the IPS and optimization of convex combinations of measures
Characterizing Pareto optimality II: partition ratios
Geometric object #2: The Radon-Nikodym set (RNS)
Characterizing Pareto optimality III: the RNS, Weller's construction, and w-association
The shape of the IPS
The relationship between the IPS and the RNS
Other issues involving Weller's construction, partition ratios, and Pareto optimality
Strong Pareto optimality
Characterizing Pareto optimality using hyperreal numbers
Gemetric object #1d: The multi-cake individual pieces set (MIPS): symmetry restored
References
Index
Symbol and Abbreviations Index

Voir tout

Replier

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Julius B. Barbanel
Parution	07/04/2005
Nb. de pages	462
Format	15,5 x 23,5
Couverture	Relié
Poids	745g
Intérieur	Noir et Blanc
EAN13	9780521842488
ISBN13	978-0-521-84248-8