On the Core of Games with Communication Structures

It is well-known that the core on several domains of cooperative transferable utility (TU) and nontransferable utility (NTU) games is characterized by various combinations of axioms containing some versions of the reduced game property, of its converse, or of the reconfirmation property with respect to the Davis-Maschler reduced game. We show that these characterizations are still valid for games with communication structures a la Myerson when using the notion of the reduced communication structure that establishes a new link between two inside players if they can communicate via outside players. Thus, it is shown that, if communication structures are present, the core may still be characterized on balanced TU games, on totally balanced TU games, on NTU games with a nonempty core, on the domains of all TU or NTU games, and on several other interesting domains of TU and NTU games. As a byproduct we construct, for any NTU game with communication structure, a certain classical NTU game with the same core that may be regarded as its Myerson restricted NTU game.