Ugo Bolletta: ugo.bolletta[at]univ-amu.fr
Mathieu Faure: mathieu.faure[at]univ-amu.fr
We show that a concept of aggregation can hold for games played on networks. We first provide a condition on a group of players in a network, called a module, which ensures that the group can behave like a single player. Furthermore, we show that a partition of players of a game into modules gives rise to an aggregate game, whose Nash equilibria, together with the Nash equilibria of the games played at the module level, correspond to Nash equilibria of the game. Then, we show that fitting aggregate games into each other in an appropriate way provides a hierarchical decomposition of the game, which can inform a recursive computation of Nash equilibria. Finally, we provide an application to the model of public goods in networks to illustrate the usefulness of our results.