Computing Solutions for Matching Games

Arbeitspapier

A matching game is a cooperative game (N; v) defined on a graph G = (N;E) with an edge weighting w : E ! R+. The player set is N and the value of a coalition S N is defined as the maximum weight of a matching in the subgraph induced by S. First we present an O(nm+n2 log n) algorithm that tests if the core of a matching game defined on a weighted graph with n vertices and m edges is nonempty and that computes a core member if the core is nonempty. This algorithm improves previous work based on the ellipsoid method and can also be used to compute stable solutions for instances of the stable roommates problem with payments. Second we show that the nucleolus of an n-player matching game with a nonempty core can be computed in O(n4) time. This generalizes the corresponding result of Solymosi and Raghavan for assignment games. Third we prove that is NP-hard to determine an imputation with minimum number of blocking pairs, even for matching games with unit edge weights, whereas the problem of determining an imputation with minimum total blocking value is shown to be polynomial-time solvable for general matching games.

Object Details

• ISBN: 978-615-5024-86-3
• Language: Englisch

References and Relationships

• Bibliographic citation: Series: IEHAS Discussion Papers ; No. MT-DP - 2011/42

Classification and Topics

• Classification: Wirtschaft ; Optimization Techniques; Programming Models; Dynamic Analysis ; Computational Techniques; Simulation Modeling ; Cooperative Games ; Bargaining Theory; Matching Theory
• Subject: matching game ; nucleolus ; cooperative game theory ; Kooperatives Spiel

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Biró, Péter ; Kern, Walter ; Paulusma, Daniël
• Event: Veröffentlichung
• (who): Hungarian Academy of Sciences, Institute of Economics
• (where): Budapest
• (when): 2011

Further information

• Handle: http://hdl.handle.net/10419/108235
• Last update: 10.03.2025, 11:42 AM CET