The Effect of Externalities Aggregation on Network Games Outcomes

We generalize results on the monotocity of equilibria for network games with incomplete information.In those games players know the stochastic process of network formation and their own degree in the realized network, and decide an action depending on the strategic interaction in the network between their own action and a statistic (as the mean, the maximum or the minimum) of neighbors' actions.We show that, even under degree independence, not only the distinction between 'strategic complements' and 'strategic substitutes' is important in determining the nature of Bayesian Nash equilibria, but also the nature itself of the statistic