An algorithm for finding the nucleolus of assignment games

Solymosi, Tamás; Raghavan, T. E. S.

doi:10.1007/bf01240179

Cited by 108 publications

(81 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We also …nd from Table 1 that, following Behringer [2], others (i.e., Dragan [3], Sankaran [16], and Solymosi and Raghavan [19]) attempted to further improve the LP method; but, they didn't …nd any method better than Behringer [2].…”

Section: Appendix B Sequential Lp Methods For Computing the Nucleolus mentioning

confidence: 99%

“…Solymosi and Raghavan's approach in [19] is only applied to a special type of cooperative games (i.e., assignment games). Potters et al [15] suggested an LP approach that may reduce the number of linear problems; but, this approach increases the size of each linear problem.…”

Section: Appendix B Sequential Lp Methods For Computing the Nucleolus mentioning

confidence: 99%

“…Raghavan [19] Algorithm to determine the nucleolus of an assignment game. In an (m; n)-person assignment game, the nucleolus is found in at most m(m + 3)=2…”

Section: Solymosi Andmentioning

confidence: 99%

See 2 more Smart Citations

Analytic solution for the nucleolus of a three‐player cooperative game

Leng¹,

Parlar²

2010

Naval Research Logistics

View full text Add to dashboard Cite

The nucleolus solution for cooperative games in characteristic function form is usually computed numerically by solving a sequence of linear programming (LP) problems, or by solving a single, but very large-scale, LP problem. This paper proposes an algebraic method to compute the nucleolus solution analytically (i.e., in closed-form) for a three-player cooperative game in characteristic function form. We …rst consider cooperative games with empty core and derive a formula to compute the nucleolus solution. Next, we examine cooperative games with non-empty core and calculate the nucleolus solution analytically for …ve possible cases arising from the relationship among the value functions of di¤erent coalitions.

show abstract

Section: Appendix B Sequential Lp Methods For Computing the Nucleolus mentioning

confidence: 99%

Section: Appendix B Sequential Lp Methods For Computing the Nucleolus mentioning

confidence: 99%

See 1 more Smart Citation

Analytic solution for the nucleolus of a three‐player cooperative game

Leng¹,

Parlar²

2010

Naval Research Logistics

View full text Add to dashboard Cite

show abstract

“…Some special cases have been studied, for instance, balanced matching games (Biró et al, 2011) or cardinality matching games, with unitary weights (Kern and Paulusma, 2003). In all these cases it is proved the nucleolus can be computed in polynomial time, what can be viewed as a generalization of the first result with an algorithm for the computation of the nucleolus of the assignment game, the bilateral case (Solymosi and Raghavan, 1994). Recently Martínez-de-Albéniz et al (2013) provides a new procedure to compute the nucleolus of the assignment game.…”

Section: Introductionmentioning

confidence: 99%

Insights into the Nucleolus of the Assignment Game

2015

View full text Add to dashboard Cite

Abstract: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.JEL Codes: C71.

show abstract

“…It is defined as the unique payoff that lexicographically minimizes the vector of nonincreasingly-ordered excesses. Solymosi and Raghavan (1994) give an algorithm to compute the nucleolus of an assignment game. It is known from Núñez (2004) that all assignment games with the same core also have the same nucleolus.…”

Section: Introductionmentioning

confidence: 99%

Assignment markets with the same core

Martínez-de-Albéniz

Núñez

Rafels

2011

Games and Economic Behavior

View full text Add to dashboard Cite

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 form a join-semilattice with a finite number of minimal elements and a unique maximum. We provide a characterization of the minimal elements. A sufficient condition under which the join-semilattice reduces to a lattice is also given.Keywords: assignment game, core, semilattice JEL: C71Resumen: En el contexto de los juegos de asignación bilaterales, estudiamos el conjunto de matrices asociadas a mercados de asignación con el mismo núcleo. Se proporcionan condiciones sobre las entradas de la matriz que aseguran que los juegos de asignación asociados tienen el mismo núcleo. Se prueba que este conjunto de matrices que dan lugar al mismo núcleo forman un semirretículo con un número finito de elementos minimales y unúnico máximo. Se da una caracterización de estos elementos minimales. También se proporciona una condición suficiente para obtener un retículo.

show abstract

An algorithm for finding the nucleolus of assignment games

Cited by 108 publications

References 11 publications

Analytic solution for the nucleolus of a three‐player cooperative game

Analytic solution for the nucleolus of a three‐player cooperative game

Insights into the Nucleolus of the Assignment Game

Assignment markets with the same core

Contact Info

Product

Resources

About