000			03348nam a22003378i 4500
001			CR9780511546679
003			UkCbUP
005			20200124160321.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090508s2005||||enk o ||1 0|eng|d
020			_a9780511546679 (ebook)
020			_z9780521842488 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA165 _b.B37 2005
082	0	0	_a512.7/3 _222
100	1		_aBarbanel, Julius B., _d1951- _eauthor.
245	1	4	_aThe geometry of efficient fair division / _cJulius B. Barbanel ; with an introduction by Alan D. Taylor.
264		1	_aCambridge : _bCambridge University Press, _c2005.
300			_a1 online resource (ix, 462 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_gIntroduction / _rAlan D. Taylor -- _g1. _tNotation and preliminaries -- _g2. _tGeometric object #1a : the individual pieces set (IPS) for two players -- _g3. _tWhat the IPS tells us about fairness and efficiency in the two-player context -- _g4. _tThe individual pieces set (IPS) and the full individual pieces set (FIPS) for the general n-player context -- _g5. _tWhat the IPS and the FIPS tell us about fairness and efficiency in the general n-player context -- _g6. _tCharacterizing Pareto optimality : introduction and preliminary ideas -- _g7. _tCharacterizing Pareto optimality I : the IPS and optimization of convex combinations of measures -- _g8. _tCharacterizing Pareto optimality II : partition ratios -- _g9. _tGeometric object #2 : the Radon-Nikodym set (RNS) -- _g10. _tCharacterizing Pareto optimality III : the RNS, Weller's construction, and w-association -- _g11. _tThe shape of the IPS -- _g12. _tThe relationship between the IPS and the RNS -- _g13. _tOther issues involving Weller's construction, partition ratios, and Pareto optimality -- _g14. _tStrong Pareto optimality -- _g15. _tCharacterizing Pareto optimality using hyperreal numbers -- _g16. _tGeometric object #1d : the multicake individual pieces set (MIPS) symmetry restored.
520			_aWhat 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	_aPartitions (Mathematics)
700	1		_aTaylor, Alan D., _d1947- _ewriter of introduction.
776	0	8	_iPrint version: _z9780521842488
856	4	0	_uhttps://doi.org/10.1017/CBO9780511546679
999			_c521916 _d521914