A description of the Shapley value using a binary procedure

Abstract

We introduce a binary recursive procedure to extend the standard solution to solve 2-player cooperative games. This procedure uses adjusted games and the binary total partitions of the set of players. We show that the resulting extension is a solution concept for n-player cooperative games which satisfies a recursive formula and we prove that this formula is satisfied by a solution concept if and only if the solution concept is the Shapley value.