In this paper we characterize convex games by means of Owen's multilinear extension and the marginal worth vectors associated with even or odd permutations. Therefore we have obtained a refinement of the classic theorem; Shapley (1971), Ichiishi (1981) in order to characterize the convexity of a...

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

We analyze assortative multisided assignment games, following Sherstyuk (1999) and Martínez-de-Albéniz et al. (2019). In them players' abilities are complementary across types (i.e. supermodular), and also the output of the essential coalitions is increasing depending on types. We study the...

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...

We prove a theorem on the intersection of the Weber sets (Weber, 1988) of two ordered cooperative games. From this theorem several consequences are derived, the inclusion of the core in the Weber set (Weber, 1988), the fact that every convex game has a large core (Sharkey, 1982), and a discrete...

In the framework of bilateral assignment games, we study the set of matrices associated with assignment markets with the same core. We state conditions on matrix entries that ensure that the related assignment games have the same core. We prove that the set of matrices leading to the same core...

A matrix A defines an assignment market, where each row represents a buyer and each column a seller. If buyer i is matched with seller j, the market produces aij units of utility. Quint (1991) points out that usually many different assignment matrices exist that define markets with the same core...