Barbanel, Julius B. and Brams, Steven J. and Stromquist, Walter (2008): Cutting a pie is not a piece of cake. Forthcoming in: American Mathematical Monthly , Vol. 116, No. June/July 2009

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Abstract
Is there a division among n players of a cake using n1 parallel vertical cuts, or of a pie using n radial cuts, that is envyfree (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 piecutting harder than cakecutting. We suggest possible applications and conclude with two open questions.
Item Type:  MPRA Paper 

Original Title:  Cutting a pie is not a piece of cake 
Language:  English 
Keywords:  Fair division; cakecutting; piecutting; divisible good; envyfreeness; allocative efficiency 
Subjects:  D  Microeconomics > D7  Analysis of Collective DecisionMaking D  Microeconomics > D6  Welfare Economics C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory 
Item ID:  12772 
Depositing User:  Steven J. Brams 
Date Deposited:  16. Jan 2009 06:55 
Last Modified:  18. Feb 2013 08:43 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/12772 