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

The European Commission’s draft of the new Corporate Sustainability Reporting Directive (CSRD) is intended to extend European sustainability reporting standards to cover all companies falling under the scope of the directive. Based on a comprehensive evaluation of non-financial statements of...