A Simple Characterization of Assignment Mechanisms on Set Constraints

Ping Zhan

SN Operations Research Forum, 2023, vol. 4, issue 2, 1-15

Abstract: Abstract We consider the problem of allocating divisible/indivisible goods to agents according to agents’ ordinal preferences. Hashimoto et al. [15] provided a nonalgorithmic and axiomatic characterization of well-studied probabilistic serial (PS) mechanism. Recently, Fujishige et al. [12] generalized the PS mechanism where goods are enlarged from a fixed set to a family of sets which is a polytope defined by a system of linear inequalities associated with submodular functions. The above extended PS (EPS) greatly improved the flexibility of allocations. Based on these two results, in this paper, we investigate the nonalgorithmic and axiomatic characterization of EPS. We show that the EPS rule is the only mechanism satisfying the ordinal fairness and a newly defined non-wastefulness. The submodularity plays a crucial role in our arguments.

Keywords: Probabilistic serial; Submodular functions; Ordinal fairness; Non-wastefulness (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s43069-023-00195-7

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