We provide explicit formulas for the nucleolus of an arbitrary assignment game with two buyers and two sellers. Five different cases are analyzed depending on the entries of the assignment matrix. We extend the results to the case of 2 x m or m x 2 assignment games.

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 give conditions to compute the extreme core allocations of a multisided assignment game. The way to compute the extreme core points rely on the extreme core points of a suitable finite family of cooperative games

We study the marginal worth vectors and their convex hull, the so-called Weber set, from the original coalitional game and the transformed one, which is called the Weber set of level k. We prove that the core of the original game is included in each of the Weber set of level k,for any k,and that...

We study the marginal worth vectors and their convex hull, the socalled Weber set, from the original coalitional game and the transformed one, which is called the Weber set of level k. We prove that the core of the original game is included in each of the Weber set of level k, for any k, and...

We study a cooperative problem where agents contribute a certain amount of input in order to obtain a surplus. We assume that the average surplus with respect to the amount contributed is increasing. Within this basic model, a cooperative game is associated and the proportional distribution...

The Böhm-Bawerk horse markets are assignment markets with homogeneous goods that are known to have a one-dimensional core. We show here that, although there exist two-sided assignment games with non-homogeneous products and with a segment as a core, the Böhm-Bawerk horse markets are the only...