Cutting a pie is not a piece of cake

Julius B. Barbanel, Steven Brams () and Walter Stromquist

MPRA Paper from University Library of Munich, Germany

Abstract: Is there a division among n players of a cake using n-1 parallel vertical cuts, or of a pie using n radial cuts, that is envy-free (each player thinks he or she receives a largest piece and so does not envy another player) and undominated (there is no other allocation as good for all players and better for at least one)? David Gale first asked this question for pies. We provide complete answers for both cakes and pies. The answers depend on the number of players (two versus three or more players) and whether the players' preferences satisfy certain continuity assumptions. We also give some simple algorithms for cutting a pie when there are two or more players, but these algorithms do not guarantee all the properties one might desire in a division, which makes pie-cutting harder than cake-cutting. We suggest possible applications and conclude with two open questions.

Keywords: Fair division; cake-cutting; pie-cutting; divisible good; envy-freeness; allocative efficiency (search for similar items in EconPapers)
JEL-codes: C7 D6 D7 (search for similar items in EconPapers)
Date: 2008-12
New Economics Papers: this item is included in nep-gth and nep-hpe
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:12772

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