On the ranking of players in Network Games with local average

We consider a network Nash equilibrium problem where players are represented as nodes of the graph of social relationships and each player’s action is influenced by the actions of her social contacts. Within this model, we investigate the problem of ranking the importance of different players. To this end, we first consider some classic topological measures, commonly used to assess the importance of nodes of a graph, and combine them using the entropy weighting method to obtain a single topological measure. We then consider a different measure of importance, based on the social welfare function, computed at the Nash equilibrium, for the original network, as well as for all the networks obtained from the initial one by removing a single player. The two measures are then illustrated and compared with the help of small size test problems