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.
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We thank Hirofumi Yamamura for comments on an earlier version, and for drawing our attention to his joint work with Fumiya Inoue. We also thank William Thomson for comments on an earlier version of the paper. The comments of two reviewers and an associate editor are gratefully acknowledged.
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Gong, D., Dietzenbacher, B. & Peters, H. Mechanisms and axiomatics for division problems with single-dipped preferences. Econ Theory (2024). https://doi.org/10.1007/s00199-023-01550-9
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DOI: https://doi.org/10.1007/s00199-023-01550-9