Brams, Steven J. and Jones, Michael A. and Klamler, Christian (2010): Divideandconquer: A proportional, minimalenvy cakecutting algorithm. Forthcoming in: SIAM Review (2011)

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Abstract
We analyze a class of proportional cakecutting algorithms that use a minimal number of cuts (n1 if there are n players) to divide a cake that the players value along one dimension. While these algorithms may not produce an envyfree or efficient allocationas these terms are used in the fairdivision literatureone, divideandconquer (D&C), minimizes the maximum number of players that any single player can envy. It works by asking n ≥ 2 players successively to place marks on a cakevalued along a linethat divide it into equal halves (when n is even) or nearly equal halves (when n is odd), then halves of these halves, and so on. Among other properties, D&C ensures players of at least 1/n shares, as they each value the cake, if and only if they are truthful. 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.
Item Type:  MPRA Paper 

Original Title:  Divideandconquer: A proportional, minimalenvy cakecutting algorithm 
Language:  English 
Keywords:  mechanism design; fair division; divisible good; cakecutting; divideandchoose 
Subjects:  D  Microeconomics > D6  Welfare Economics > D63  Equity, Justice, Inequality, and Other Normative Criteria and Measurement D  Microeconomics > D7  Analysis of Collective DecisionMaking > D74  Conflict ; Conflict Resolution ; Alliances ; Revolutions C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory 
Item ID:  22704 
Depositing User:  Steven J. Brams 
Date Deposited:  17 May 2010 13:38 
Last Modified:  27 Sep 2019 16:26 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/22704 