Digraph competitions and cooperative games (Q1403964)

The authors consider the model of a fixed finite set \(N\) of nodes with domination structure described by a directed graph \(D \subset N \times N\) (\textit{digraph competition}). The purpose of the paper is to propose a new procedure determining the power of each node. To this end, a cooperative TU-game (\textit{digraph game}) is defined, strictly related with a digraph \(D\). Next the Shapley value, the core and a selectope of a digraph game are found and discussed. Also some remarks about possible weighted digraph competitions are given. The results of the paper are illustrated with two examples of digraph competitions where the Shapley value is applied to evaluate the strength of posistions. The first one analyzes the situation of the UFFA European Soccer Championship (EURO 2000). The second example discusses an application to the ranking of alternatives in social choice theory.