[MD-sorular] Cake cutting problem

[Ali Ýlik]

Alttaki maili yolladığım tarih 18 Şubat 2007. Brams aynı gün yanıtladı.
"Attached" dediÄŸi file 221 KB. ve listeye gitmedi. Mailleri ve attached
olarak bana yolladığı son makalesinin Abstract'ını ekliyorum en altta. İlgi
duyanlar faydalansın. Zira bazen bir sorunun yanıtının bilinip bilinmediğini
anlamanın en iyi yollarından biri o alanda çalışan uzmanlara sormaktır.
Bazen soru öylesine spesifiktir ki dünyada bir iki kişi ya bilir ya bilmez
sorunun tarihsel geçmişini...

"
 Dear Ali,


      To the best of my knowledge, the answer is no for n > 3, though Su
(1999) offers an approximate approach to this problem.  In a recent paper,
which I've attached, my coauthors and I analyze a simple proportional
procedure,  divide-and-conquer, but it is neither envy-free nor efficient.


      Best wishes,
      Steven Brams
 - Tırnak içindeki metni gizle -



Hi Sir,



I have read your article on AMS Notices "Better Ways to Cut a Cake"



I am a Sophomore student at www.uludag.edu.tr dept of math. I am trying to
write a popluar math article about cake cutting.



Well, not a technical article but something, kind
of mathematical, explaining cake cutting problem.



I wonder if the following question is still open:



"Is there any finite, bounded procedure for envy free cake division?"



I know u must be very busy with your articles, courses etc.



Yet even any short answer from you such as "yes, it is still open" or "no,
it has been solved and the answer is given in the article titled...or on
the link..."



Thank you so much.



Your sincerely,


--
Ali ilik








-- 

Steven J. Brams         Phone:   (212) 998-8510
Dept. of Politics                FAX:       (212) 995-4184
19 West 4th St., 2d Fl.                E-mail:   steven.brams at nyu.edu
New York University
New York, NY  10012 <--------------Note new mailing address (01/07)
"
--


"

* *

*Divide-and-Conquer:*

*A Proportional, Minimal-Envy Cake-Cutting Procedure***

* *

Steven J. Brams

Department of Politics

New York University

New York, NY  10003

UNITED STATES

steven.brams at nyu.edu <Steven.brams at nyu.edu>



Michael A. Jones

Department of Mathematics

Montclair State University

Montclair, NJ  07043

UNITED STATES

jonesm at mail.montclair.edu



Christian Klamler

Institute of Public Economics

University of Graz

A-8010 Graz

AUSTRIA

christian.klamler at uni-graz.at











February 2007**
*
*

*Abstract*

Properties of discrete cake-cutting procedures that use a minimal number of
cuts (*n* – 1 if there are *n* players) are analyzed.  None is always
envy-free or efficient, but divide-and-conquer (D&C) minimizes the maximum
number of players that any single player may envy.  It works by asking *n ≥
*2 players successively to place marks on a cake that divide it into equal
or approximately equal halves, then halves of these halves, and so on.  Among
other properties, D&C (i) ensures players of more than 1/*n* shares if their
marks are different and (ii) is strategyproof for risk-averse players.
 However,
D&C may not allow players to obtain proportional, connected pieces if they
have unequal entitlements.  Possible applications of D&C to land division
are briefly discussed.
"
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