VALUES FOR GAMES ON THE CYCLES OF A DIGRAPH

Abstract

In this paper we introduce a new class of cooperative games. We define a characteristic function over the cycles of a digraph. We present a mathematical model for this situation and an axiomatic characterization of a solution for this class of cooperative games. This is introduced as a method to measure the importance of the nodes in a digraph, and can be related with the Shapley value of a game in characteristic function form. Also, we extend the modeling by applying coalitional structures for the nodes and r-efficient solutions, where the allocation amount is a real number r, showing axiomatic solutions in both cases.