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 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 prove that for any coalitional game the core coincides with the bargaining set à la Davis and Maschler when we sufficiently raise the worth of the grand coalition (the efficiency level). This coincidence result does not hold for other well-known bargaining sets like the Mas-Colell bargaining...

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...

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...