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...

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

Let N = {1,..., n} be a finite set of players and KN the complete graph on the node set N "union" {0}. Assume that the edges of KN have nonnegative weights and associate with each coalition S "subset of" N of players as cost c(S) the weight of a minimal spanning tree on the node set S "union"...