Consistency and Monotonicity in One-Sided Assignment Problems

Bettina Klaus () and Alexandru Nichifor ()
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Alexandru Nichifor: Department of Economics, Maastricht University

No 09-146, Harvard Business School Working Papers from Harvard Business School

Abstract: 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.

Keywords: (One-sided) assignment problems; consistency; core; matching. (search for similar items in EconPapers)
JEL-codes: C71 C78 D63 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2009-06
New Economics Papers: this item is included in nep-gth
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Citations: View citations in EconPapers (1)

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