The geometry of efficient fair division / (Record no. 521916)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03348nam a22003378i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9780511546679 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200124160321.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 090508s2005||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780511546679 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9780521842488 (hardback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA165 |
| Item number | .B37 2005 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.7/3 |
| Edition number | 22 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Barbanel, Julius B., |
| Dates associated with a name | 1951- |
| Relator term | author. |
| 245 14 - TITLE STATEMENT | |
| Title | The geometry of efficient fair division / |
| Statement of responsibility, etc | Julius B. Barbanel ; with an introduction by Alan D. Taylor. |
| 264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R) | |
| Place of production, publication, distribution, manufacture (R) | Cambridge : |
| Name of producer, publisher, distributor, manufacturer (R) | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2005. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (ix, 462 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - Content Type (R) | |
| Content type term (R) | text |
| Content type code (R) | txt |
| Source (NR) | rdacontent |
| 337 ## - Media Type (R) | |
| Media type term (R) | computer |
| Media type code (R) | c |
| Source (NR) | rdamedia |
| 338 ## - Carrier Type (R) | |
| Carrier type term (R) | online resource |
| Carrier type code (R) | cr |
| Source (NR) | rdacarrier |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 00 - FORMATTED CONTENTS NOTE | |
| Miscellaneous information | Introduction / |
| Statement of responsibility | Alan D. Taylor -- |
| Miscellaneous information | 1. |
| Title | Notation and preliminaries -- |
| Miscellaneous information | 2. |
| Title | Geometric object #1a : the individual pieces set (IPS) for two players -- |
| Miscellaneous information | 3. |
| Title | What the IPS tells us about fairness and efficiency in the two-player context -- |
| Miscellaneous information | 4. |
| Title | The individual pieces set (IPS) and the full individual pieces set (FIPS) for the general n-player context -- |
| Miscellaneous information | 5. |
| Title | What the IPS and the FIPS tell us about fairness and efficiency in the general n-player context -- |
| Miscellaneous information | 6. |
| Title | Characterizing Pareto optimality : introduction and preliminary ideas -- |
| Miscellaneous information | 7. |
| Title | Characterizing Pareto optimality I : the IPS and optimization of convex combinations of measures -- |
| Miscellaneous information | 8. |
| Title | Characterizing Pareto optimality II : partition ratios -- |
| Miscellaneous information | 9. |
| Title | Geometric object #2 : the Radon-Nikodym set (RNS) -- |
| Miscellaneous information | 10. |
| Title | Characterizing Pareto optimality III : the RNS, Weller's construction, and w-association -- |
| Miscellaneous information | 11. |
| Title | The shape of the IPS -- |
| Miscellaneous information | 12. |
| Title | The relationship between the IPS and the RNS -- |
| Miscellaneous information | 13. |
| Title | Other issues involving Weller's construction, partition ratios, and Pareto optimality -- |
| Miscellaneous information | 14. |
| Title | Strong Pareto optimality -- |
| Miscellaneous information | 15. |
| Title | Characterizing Pareto optimality using hyperreal numbers -- |
| Miscellaneous information | 16. |
| Title | Geometric object #1d : the multicake individual pieces set (MIPS) symmetry restored. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Partitions (Mathematics) |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Taylor, Alan D., |
| Dates associated with a name | 1947- |
| Relator term | writer of introduction. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| International Standard Book Number | 9780521842488 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9780511546679">https://doi.org/10.1017/CBO9780511546679</a> |
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