A procedure to compute the nucleolus of the assignment game

The assignment game introduced by Shapley and Shubik (1972) 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 goods. 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 fewer agents

A note on assignment games with the same nucleolus

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

Assortative multisided assignment games. The extreme core points [WP]

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 extreme core points and show a simple mechanism to compute all of them. In this way we describe the whole core. This mechanism works from the original data array and the maximum number of extreme core points is obtained

Insights into the nucleolus of the assignment game

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

The nucleolus of the assignment game. Structure of the family

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

Solving Becker's assortative assignments and extensions

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

On the nucleolus of 2 x 2 assignment games (WP)

[spa] En este artículo hallamos fórmulas para el nucleolo de juegos de asignación arbitrarios con dos compradores y dos vendedores. Se analizan cinco casos distintos, dependiendo de las entradas en la matriz de asignación. Los resultados se extienden a los casos de juegos de asignación de tipo 2 x m o m x 2.[eng] 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 × m or m × 2 assignment games

Assortative multisided assignment games: the extreme core points

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 extreme core points and show a simple mechanism to compute all of them. In this way we describe the whole core. This mechanism works from the original data array and the maximum number of extreme core points is obtained

On the nucleolus of 2 x 2 assignment games

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 2xm or mx2 assignment games

Solving Becker's assortative assignments and extensions

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