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...

The stable roommates problem with payments has as input a graph G(E,V) with an edge weighting w:E_ùR+ and the problem is to find a stable solution. A solution is a matching M with a vector p.RV that satisfies pu+pv=w(uv) for all uv.M and pu=0 for all u unmatched in M. A solution is stable if it...

We generalize two well-known game-theoretic models by introducing multiple partners matching games, defined by a graph G = (N;E), with an integer vertex capacity function b and an edge weighting w. The set N consists of a number of players that are to form a set M is a subset of E of 2-player...

The stable roommates problem with payments has as input a graph G(E,V) with an edge weighting w:E→R+ and the problem is to find a stable solution. A solution is a matching M with a vector pϵRV that satisfies 􂀀pu+pv=w(uv) for all uvϵM and pu=0 for all u unmatched in M. A solution is stable...

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 C̱ 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...

A simple game (N,v) is given by a set N of n players and a partition of 2N into a set L of losing coalitions L with value v(L) = 0 that is closed under taking subsets and a set W of winning coalitions W with v(W) = 1. Simple games with α = minp>0 maxW∈W,L∈L p(L) p(W) < 1 are exactly the weighted voting games. We show that α 6 1 4n for every simple game (N,v), confi rming the conjecture of Freixas and Kurz (IJGT, 2014). For complete simple games, Freixas and Kurz conjectured that α = O(√n). We prove this conjecture up to a ln n factor. We also prove that for graphic simple games, that is, simple games in which every minimal winning coalition has size 2, computing α is NP-hard, but polynomial-time solvable if the underlying graph is bipartite. Moreover, we show that for every graphic simple game, deciding if α < a is polynomial-time solvable for every fixed a > 0