The P-core

Abstract

In many of the extensions of the core of a game with transferable utility to non-balanced games thesubjacent idea is to construct first a related balanced game, and then, to take its core as an extended core notion for the original non-balanced game. The "-core and the aspiration core are two examples of this methodology. While the balanced game related to the "-core is gotten by reducing in a positive amount " the value of any non-empty coalition different from the grand coalition, the balanced game related to the aspiration core is obtained by increasing the value of the grand coalition by an appropriate quantity. In both cases, the balanced game obtained is not an orthogonal projection of the original game onto the cone of balanced games. We propose a new extension which uses, as an auxiliary balanced game, a game which is, indeed, an orthogonal projection of the original game on the cone of balanced games. In this projected game, the value of the grand coalition increases while the value of some of the others coalitions decreases.