Aggregation in Networks

In this paper, we show that a concept of aggregation can hold in large network games with linear best replies. Breaking up large networks into smaller subnetworks, which can be replaced by representative players, leads to a coarse-grained description of strategic interactions. This method of summarizing complex strategic interactions by simple ones can be applied to compute all Nash equilibria for the special network structure of cograph. A key finding is that a stable Nash equilibrium of the large network game can be decomposed into a collection of Nash equilibria of subnetwork games. Thereby, we establish a systematic relationship between player’s position in a subnetwork and his equilibrium action in the large network game.