RT Journal Article
T1 On the Set of Balanced Games
A1 García Segador, Pedro
A1 Grabisch, Michel
A1 Miranda Menéndez, Pedro
AB 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 this set is a nonpointed polyhedral cone, and we find the set of its extremal rays and facets. This study is also done for the set of balanced games whose value for the grand coalition is fixed, which yields an affine nonpointed polyhedral cone. Finally, the case of nonnegative balanced games with fixed value for the grand coalition is tackled. This set is a convex polytope, with remarkable properties. We characterize its vertices and facets, study the adjacency structure of vertices, develop an algorithm for generating vertices in a random uniform way, and show that this polytope is combinatorial and its adjacency graph is Hamiltonian. Last, we give a characterization of the set of games having a core reduced to a singleton.
PB Institute for Operations Research and Management Sciences
SN 0364-765X
SN 1526-5471
YR 2025
FD 2025
LK https://hdl.handle.net/20.500.14352/125809
UL https://hdl.handle.net/20.500.14352/125809
LA eng
NO Pedro Garcia-Segador, Michel Grabisch, Pedro Miranda. On the Set of Balanced Games. Mathematics of Operations Research. 2024; 50(3):2047-2072.
NO Gobierno de España
DS Docta Complutense
RD 25 mar 2026