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...

We show that the family of assignment matrices which give rise to the same nucleolus forms a compact join-semilattice with one maximal element. The above family is in general not a convex set, but path-connected