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Mechanisms and axiomatics for division problems with single-dipped preferences

Author

Listed:
  • Doudou Gong

    (Nanjing University of Science and Technology)

  • Bas Dietzenbacher

    (Maastricht University)

  • Hans Peters

    (Maastricht University)

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 main result is that when the mechanism satisfies anonymity, monotonicity, the zero–one property, and order preservation, then the Pareto optimal Nash and strong equilibria coincide and result in 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. A second main result is an axiomatic characterization of the associated social choice correspondence as the maximal correspondence satisfying minimal envy Pareto optimality, equal division lower bound, and sharing index order preservation.

Suggested Citation

  • Doudou Gong & Bas Dietzenbacher & Hans Peters, 2024. "Mechanisms and axiomatics for division problems with single-dipped preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(3), pages 789-813, November.
    • Handle: RePEc:spr:joecth:v:78:y:2024:i:3:d:10.1007_s00199-023-01550-9
    DOI: 10.1007/s00199-023-01550-9
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    More about this item

    Keywords

    Division problems; Single-dipped preferences; Mechanisms; Nash equilibrium; Strong equilibrium;
    All these keywords.

    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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