# English, Article, Journal or magazine article edition: Consistency and Monotonicity in One-Sided Assignment Problems Bettina-Elisabeth Klaus; Alexandru Nichifor

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Bookmark: http://trove.nla.gov.au/version/121627
Physical Description
• preprint
Language
• English

### Edition details

Title
• Consistency and Monotonicity in One-Sided Assignment Problems
Author
• Bettina-Elisabeth Klaus
• Alexandru Nichifor
Physical Description
• preprint
Notes
• One-sided assignment problems combine important features of two well-known matching models. First, as in roommate problems, any two agents can be matched and second, as in two-sided assignment problems, the payoffs of a matching can be divided between the agents. We take a similar approach to one-sided assignment problems as Sasaki (1995) for two-sided assignment problems and we analyze various desirable properties of solutions including consistency and weak pairwise-monotonicity. We show that for the class of solvable one-sided assignment problems (i.e., the subset of one-sided assignment problems with a non-empty core), if a subsolution of the core satisfies [indifference with respect to dummy agents, continuity, and consistency] or [Pareto indifference and consistency], then it coincides with the core (Theorems 1 and 2). However, we also prove that on the class of all one-sided assignment problems (solvable or not), no solution satisfies consistency and coincides with the core whenever the core is non-empty (Theorem 3). Finally, we comment on the difficulty in obtaining further positive results for the class of solvable one-sided assignment problems in line with Sasaki's (1995) characterizations of the core for two-sided assignment problems.
• (One-sided) assignment problems, consistency, core, matching.
• RePEc:hbs:wpaper:09-146
Language
• English
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