Consistency and monotonicity in one-sided assignment problems
By: Bettina Klaus, Alexandru Nichifor
Contributors: Nichifor, Alexandru; Harvard Business School
Series: Working paper / Harvard Business School -- 09-146; Working paper (Harvard Business School) -- 09-146.
Publisher: Harvard Business School
Published: 2009
Place of publication: [Boston]
Language: eng
Number of pages: 18
Description: One-sided assignment problems combine important features of two well-known matching models. 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, 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.
Notes: "June 2009"--Publisher's website.

Includes bibliographical references.