Extended Random Assignment Mechanisms on a Family of Good Sets

Sano, Yoshio; Zhan, Ping

doi:10.1007/s43069-021-00095-8

Oper. Res. Forum

2021

DOI: 10.1007/s43069-021-00095-8

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Extended Random Assignment Mechanisms on a Family of Good Sets

Yoshio Sano

Ping Zhan

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Cited by 3 publications

References 28 publications

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Simultaneous eating algorithm and greedy algorithm in assignment problems

Zhan

2023

J Comb Optim

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The simultaneous eating algorithm (SEA) and probabilistic serial (PS) mechanism are well known for allocating a set of divisible or indivisible goods to agents with ordinal preferences. The PS mechanism is SEA at the same eating speed. The prominent property of SEA is ordinal efficiency. Recently, we extended the PS mechanism (EPS) from a fixed quota of each good to a variable varying in a polytope constrained by submodular functions. In this article, we further generalized some results on SEA. After formalizing the extended ESA (ESEA), we show that it can be characterized by ordinal efficiency. We established a stronger summation optimization than the Pareto type of ordinal efficiency by an introduced weight vector. The weights in the summation optimization coincide with agents’ preferences at the acyclic positive values of an allocation. Hence, the order of goods selected to eat in ESEA is exactly the one chosen in the execution of the well-known greedy algorithm.

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Simultaneous eating algorithm and greedy algorithm in assignment problems

Zhan

2023

J Comb Optim

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Ex ante and ex post envy-freeness on polytope resources

Sano,

Zhan

2024

Japan J. Indust. Appl. Math.

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A Simple Characterization of Assignment Mechanisms on Set Constraints

Zhan

2023

Oper. Res. Forum

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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.

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Extended Random Assignment Mechanisms on a Family of Good Sets

Cited by 3 publications

References 28 publications

Simultaneous eating algorithm and greedy algorithm in assignment problems

Simultaneous eating algorithm and greedy algorithm in assignment problems

Ex ante and ex post envy-freeness on polytope resources

A Simple Characterization of Assignment Mechanisms on Set Constraints

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