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Divide-and-conquer: A proportional, minimal-envy cake-cutting algorithm

Author

Listed:
  • Brams, Steven J.
  • Jones, Michael A.
  • Klamler, Christian

Abstract

We analyze a class of proportional cake-cutting algorithms that use a minimal number of cuts (n-1 if there are n players) to divide a cake that the players value along one dimension. While these algorithms may not produce an envy-free or efficient allocation--as these terms are used in the fair-division literature--one, divide-and-conquer (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 cake--valued along a line--that 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.

Suggested Citation

  • Brams, Steven J. & Jones, Michael A. & Klamler, Christian, 2010. "Divide-and-conquer: A proportional, minimal-envy cake-cutting algorithm," MPRA Paper 22704, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:22704
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    File URL: https://mpra.ub.uni-muenchen.de/22704/1/MPRA_paper_22704.pdf
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    References listed on IDEAS

    as
    1. Steven Brams & Michael Jones & Christian Klamler, 2008. "Proportional pie-cutting," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 353-367, March.
    2. Barbanel, Julius B. & Brams, Steven J., 2010. "Two-person pie-cutting: The fairest cuts," MPRA Paper 22703, University Library of Munich, Germany.
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    Cited by:

    1. Brams, Steven J. & Jones, Michael A. & Klamler, Christian, 2011. "N-Person cake-cutting: there may be no perfect division," MPRA Paper 34264, University Library of Munich, Germany.

    More about this item

    Keywords

    mechanism design; fair division; divisible good; cake-cutting; divide-and-choose;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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