Multiple-aggregate Games

Consider an environment in which individuals are organised into groups, they contribute to the collective action of their group, and are influenced by the collective actions of other groups; there are externalities between groups that are transmitted through the aggregation of groups’ actions. The theory of 'aggregative games' has been successfully applied to study games in which players' payoffs depend only on their own strategy and a single aggregation of all players' strategies, but the setting just described features multiple aggregations of actions—one for each group—in which the nature of the intra-group strategic interaction may be very different to the inter-group strategic interaction. The aim of this contribution is to establish a framework within which to consider such 'multiple aggregate games'; present a method to analyse the existence and properties of Nash equilibria; and to discuss some applications of the theory to demonstrate how useful the technique is for analysing strategic interactions involving individuals in groups.