Mechanisms and axiomatics for division problems with single-dipped preferences

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 a...

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Bibliographic Details
Published in:Economic theory 2024-11, Vol.78 (3), p.789-813
Main Authors: Gong, Doudou, Dietzenbacher, Bas, Peters, Hans
Format: Article
Language:English
Subjects:
Commodities
Economic theory
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Envy
Equilibrium
Game Theory
Microeconomics
Pareto optimum
Preferences
Preservation
Public Finance
Research Article
Social and Behav. Sciences
Social choice
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Summary: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.
ISSN:0938-2259
1432-0479
DOI:10.1007/s00199-023-01550-9