4 papers
Polyhedral Methods for Cooperative Games: Small Lifts and Hard Faces
Hans Raj Tiwary, Michel Grabisch
We study the computational complexity of fundamental algorithmic problems -- membership testing, separation, valid-inequality testing, and linear optimization -- over polytopes and…
On the closest balanced game
Pedro García-Segador, Michel Grabisch, Dylan Laplace Mermoud +1
Cooperative games with nonempty core are called balanced, and the set of balanced games is a polyhedron. Given a game with empty core, we look for the closest balanced game, in the…
On the Set of Balanced Games
Pedro Garcia-Segador, Michel Grabisch, Pedro Miranda
We study the geometric structure of the set of cooperative transferable utility games having a nonempty core, characterized by Bondareva and Shapley as balanced games. We show that…
Polynomial representation of TU-games
Ulrich Faigle, Michel Grabisch
We propose in this paper a polynomial representation of TU-games, fuzzy measures, capacities, and more generally set functions. Our representation needs a countably infinite set of…