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.
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number
12772.
Find related papers by JEL classification: D7 - Microeconomics - - Analysis of Collective Decision-Making D6 - Microeconomics - - Welfare Economics C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Brams, Steven J. & Taylor, Alan D. & Zwicker, William S., 1994.
"Old and NewMoving-Knife Schemes,"
Working Papers
94-30, C.V. Starr Center for Applied Economics, New York University.
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