A note on the ''corelessness'' or antibalance of a game (Q1074514)

The characteristic function of a market game has the special property that the game is totally balanced. Every one of the \(2^ n-1\) nonempty subgames which can be formed with the n players on an n-person market game has a core. No matter what groups are considered, there is always some set of imputations at which all gain and no other group can do better for its members. The core leaves room for the bargain where all subgroups can have their ''we can go it alone'' claims satisfied. When an economy with an efficient price system is modeled as a game, the resultant game is totally balanced. There appears to be an intimate relationship between the design of an economic mechanism that can be efficiently run by prices and totally balanced games. In contrast with market games, simple games portray voting situations and in general have no core. In this paper we investigate how antibalanced a game can be; what is the maximum number of subgames of a symmetric game that can be without a core.