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Consistency and Monotonicity in One-Sided Assignment Problems

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Author Info

  • Bettina-Elisabeth Klaus

    ()
    (Harvard Business School, Negotiation, Organizations & Markets Unit)

  • Alexandru Nichifor

    ()
    (Department of Economics, Maastricht University)

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.

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Bibliographic Info

Paper provided by Harvard Business School in its series Harvard Business School Working Papers with number 09-146.

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Length: 19 pages
Date of creation: Jun 2009
Date of revision:
Handle: RePEc:hbs:wpaper:09-146

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Keywords: (One-sided) assignment problems; consistency; core; matching.;

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Cited by:
  1. Talman, A.J.J. & Yang, Z.F., 2008. "A Model of Partnership Formation," Discussion Paper 2008-103, Tilburg University, Center for Economic Research.

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