The assignment game [6] is a model for a two-sided market where there is an exchange of indivisible goods for money and buyers or sellers demand or supply exactly one unit of the good. We give a procedure to compute the nucleolus of any assignment game, based on the distribution of equal amounts to the agents, until the game is reduced to less agents.

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Abstract:We show that the family of assignment matrices which give rise to the same nucleolus form a compact join-semilattice with one maximal element, which is always a valuation (see p.43, Topkis (1998)). We give an explicit form of this valuation matrix. The above family is in general not a convex set, but path-connected, and we construct minimal elements of this family. We also analyze the conditions to ensure that a given vector is the nucleolus of some assignment game.JEL Codes: C71.

Abstract:We analyze assortative assignment games, introduced in Becker (1973) and Eriksson et al. (2000). We study the extreme core points and show an easy way to compute them. We find a natural solution for these games. It coincides with several well-known point solutions, the median stable utility solution (Schwarz and Yenmez, 2011) and the nucleolus (Schmeidler, 1969).We also analyze the behavior of the Shapley value. We finish with some extensions, where some hypotheses are relaxed.JEL Codes: C71.