The boundary of the core of a balanced game: face games

Abstract

This paper extends the concept of face games, introduced by Gonzalez-Diaz and Sanchez-Rodriguez (Games Econ Behav 62:100–105, 2008) for convex games, to the general class of balanced games. Each face of the core is the core of a face game and contains the best stable allocations for a coalition provided that the members of the complement coalition get their miminum worth inside the core. Since face games are exact we investigate several properties of the exact envelope of a balanced game that allow us to characterize exactness, convexity and decomposability of a game in terms of its face games. The close connection between extreme points of the core and extreme points of the face games is analyzed. In particular, we show that the marginal vectors that belong to the core and the lexinal vectors must be marginal vectors and lexinal vectors, respectively, of the single player face games. Finally, we present several subclasses of games where face games could provide some insight on the core structure.