each other according to a structured network of interactions. This network can represent friendships in a social network, transactions among firms in a market, or communication links in a process of belief formation. In this context, an interesting question is to study how the network structure affects the outcome of the interactions of the agents. With this purpose, one can model strategic interactions in a networked society as a multi-player simultaneous-move game. In particular, we focus our attention on the broad class of games with linear best response function [@FT91]. This class of games have been used to model various settings such as belief formation [@AP07], peer effects [@BCZ06], and public goods [@BK07].

In order to analyze the influence of the network structure on the game outcome, we use two recent results by Bramoullé et al. [@BKA10] and Ballester et al. [@BC07] relating the Nash equilibria of the game with the largest and smallest eigenvalues of the adjacency matrix of interactions. For example, in [@BKA10], the authors show that uniqueness and stability of a Nash equilibrium in games with linear best responses can be determined by the smallest eigenvalue of the network. In [@BKA10], it was also illustrated how the 