On the Reduced Game of Some Linear Production Games

Abstract

In view of the importance of reduced games in cooperative game theory, it is interesting to find out whether they have any meaning in applications. Accordingly we investigate in this paper the Davis-Maschler reduced game of some linear production games. We introduce the extended linear production game model, which generalizes Owen’s linear production game model. We show that the Davis-Maschler reduced game of the extended linear production game, calculated at a core point, is a game of the same type, and we provide some sufficient conditions for the nonemptiness of the core of this game. We further investigate the (Davis-Maschler) reduced game of some network games. In particular, we prove that the reduced game of a simple network game, at a core point, is a simple network game and that the core of the reduced game of a simple network game, for any coalition and a core vector, coincides with the set of dual optimal solutions to an associated linear programming problem.