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Forum"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider the problem of allocating divisible\/indivisible goods to agents according to agents\u2019 ordinal preferences. Hashimoto et al. [15] provided a nonalgorithmic and axiomatic characterization of well-studied <jats:italic>probabilistic serial<\/jats:italic> (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 <jats:italic>extended PS<\/jats:italic> (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 <jats:italic>only<\/jats:italic> mechanism satisfying the <jats:italic>ordinal fairness<\/jats:italic> and a newly defined <jats:italic>non-wastefulness<\/jats:italic>. The submodularity plays a crucial role in our arguments.<\/jats:p>","DOI":"10.1007\/s43069-023-00195-7","type":"journal-article","created":{"date-parts":[[2023,3,18]],"date-time":"2023-03-18T09:02:36Z","timestamp":1679130156000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Simple Characterization of Assignment Mechanisms on Set Constraints"],"prefix":"10.1007","volume":"4","author":[{"given":"Ping","family":"Zhan","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,3,18]]},"reference":[{"key":"195_CR1","doi-asserted-by":"crossref","unstructured":"Amanatidis G, Aziz H, Birmpas G, Filos-Ratsikas A, Li B, Moulin H, Voudouris A, Wu X (2022)\u00a0Fair division of indivisible goods: a survey.\u00a0Preprint at\u00a0https:\/\/arxiv.org\/abs\/2202.07551","DOI":"10.24963\/ijcai.2022\/756"},{"key":"195_CR2","unstructured":"Aziz H, Brandl F (2021) The vigilant eating rule: a general approach for probabilistic economic design with constraints. http:\/\/arxiv-export-lb.library.cornell.edu\/pdf\/2008.08991"},{"key":"195_CR3","volume":"203","author":"I Balbuzanov","year":"2022","unstructured":"Balbuzanov I (2022) Constrained random matching. 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