The P-core and some related computational procedures

Abstract

In many of the extensions of the core of a game with trans-ferable utility to non-balanced games the subjacent idea is to constructrst a related balanced game, and then, to take its core as an extendedcore notion for the original non-balanced game. The "-core and the as-piration core are two examples of this methodology. While the balancedgame related to the "-core is gotten by reducing in a positive amount "the value of any non-empty coalition dierent 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 theoriginal 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 increaseswhile the value of some of the others coalitions decreases. In this note we explore some computational procedures to get the projected game.