A method for estimating the core of root game

Arina N. Akimova, Viktor V. Zakharov

Faculty of Applied Mathematics and Control Processes, St. Petersburg State University

Abstract: It is showen that the base of grand (shadow) subcore coincides with the core of the root game in any TU-cooperative game. Comparing definitions of grand subcore and grand shadow subcore with description of aggregate-monotonic core leads to the formal geometrical coincidence of aggregate-monotonic core with either grand subcore or grand shadow subcore. The method for estimating the simplest set of equations and inequalities describing the core of a root game in TU-game with any number of players ($n\ge3$) is proposed. To develop the method dual theory and inductive method by B. Peleg are used.

Keywords: TU-cooperative game, core, grand (shadow) subcore, root game, aggregate-monotonic core, linear programming, balanced collection of coalitions.

UDC: 519.83
BBK: 22.18