search-white-svg
Meine Position
i
Ein Tipp vom Eldar Team
Je mehr Sie bestellen, desto grösser Ihr Rabatt
Lieferbar
The Geometry of Efficient Fair Division
Buch
print_book
Fachbuch
2005

The Geometry of Efficient Fair Division

ISBN
EAN
978-0-521-84248-8
9780521842488
Artikel-Nr.
NDPZRW
Kostenloser Versand
CHF
187.97
Anzahl
1
Maximale
Lieferzeit
17
Arbeitstage
Donnerstag
17.02.2022
speech-bubble-svg Beschreibung
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 (is there another partition that would make everyone at least as happy, and would make at least one player happier, than the present partition?) and fairness properties (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.
Zielgruppe
Professional & Vocational
Inhaltsverzeichnis

0. Preface; 1. Notation and preliminaries; 2. Geometric object #1a: the individual pieces set (IPS) for two players; 3. What the IPS tells us about fairness and efficiency in the two-player context; 4. The general case of n players; 5. What the IPS and the FIPS tell us about fairness and efficiency in the n-player context; 6. Characterizing Pareto optimality: introduction and preliminary ideas; 7. Characterizing Pareto optimality I: the IPS and optimization of convex combinations of measures; 8. Characterizing Pareto optimality II: partition ratios; 9. Geometric object #2: The Radon-Nikodym set (RNS); 10. Characterizing Pareto optimality III: the RNS, Weller's construction, and w-association; 11. The shape of the IPS; 12. The relationship between the IPS and the RNS; 13. Other issues involving Weller's construction, partition ratios, and Pareto optimality; 14. Strong Pareto optimality; 15. Characterizing Pareto optimality using hyperreal numbers; 16. The multi-cake individual pieces set (MIPS): symmetry restored.

Publikation
2005
book-svg Format
Hardcover
472 Seiten
package-svg Versand
Kostenloser Versand: Schweiz & Liechtenstein
Für den Versand nach Deutschland oder Frankreich werden die Versandgebühren der Schweizerischen Post berechnet. Diese werden Ihnen im Warenkorb für Ihre gesamte Bestellung berechnet.
credit-card-svg Zahlungsarten
payment-einzahlungsschein payment-twint payment-mastercard payment-visa payment-american-express
Bestellen Sie einfach auf Rechnung oder bezahlen Sie bequem und gebührenfrei mit Twint oder Kreditkarte.
subcategories-svg
Passende Themen
Unterkategorie
Geometrie
arrow-right-top-svg
Zurück
Zum Start
S
SPIEGEL Bestseller
Hauptkategorie