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Mechanisms for division problems with single-dipped preferences

Author

Listed:
  • Gong, Doudou

    (RS: GSBE other - not theme-related research, Quantitative Economics)

  • Dietzenbacher, Bas

    (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory)

  • Peters, Hans

    (RS: FSE DKE Mathematics Centre Maastricht, QE Math. Economics & Game Theory)

Abstract

A mechanism allocates one unit of an infinitely divisible commodity among agents reporting a number between zero and one. Nash, Pareto optimal Nash, and strong equilibria are analyzed for the case where the agents have single-dipped preferences. One of the main results is that when the mechanism is anonymous, monotonic, standard, and order preserving, then the Pareto optimal Nash and strong equilibria coincide and assign Pareto optimal allocations that are characterized by so-called maximal coalitions: members of a maximal coalition prefer an equal coalition share over obtaining zero, whereas the outside agents prefer zero over obtaining an equal share from joining the coalition.

Suggested Citation

  • Gong, Doudou & Dietzenbacher, Bas & Peters, Hans, 2022. "Mechanisms for division problems with single-dipped preferences," Research Memorandum 007, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2022007
    DOI: 10.26481/umagsb.2022007
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    References listed on IDEAS

    as
    1. Bossert, Walter & Peters, Hans, 2014. "Single-basined choice," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 162-168.
    2. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    3. Grisel Ayllón & Diego M. Caramuta, 2016. "Single-dipped preferences with satiation: strong group strategy-proofness and unanimity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 245-264, August.
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    Cited by:

    1. Yamamura, Hirofumi, 2023. "Uniform rules for the allocation problem with single-dipped preferences when free-disposal is possible," Economics Letters, Elsevier, vol. 230(C).
    2. Dietzenbacher, Bas & Tamura, Yuki, 2023. "Fair and efficient allocations when preferences are single-dipped," Research Memorandum 009, Maastricht University, Graduate School of Business and Economics (GSBE).
    3. Dietzenbacher, Bas & Tamura, Yuki, 2023. "Stable and efficient reallocations when preferences are single-dipped," Economics Letters, Elsevier, vol. 231(C).

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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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