A Theory of Network Games

Abstract

We study games in which strategic interactions are bilateral in the following sense: if an opponent j switching from action s j to action s ′ j causes i's preferences between s i and s ′ i to flip for some profile of other players' actions, then player j switching from s j to s ′ j cannot cause i's preferences between s i and s ′ i to flip in the opposite direction at any alternative profile of other players' actions. Subject to richness conditions on opponent actions, this implies that for any two actions of player i, we can represent her preferences between them using a utility that is additively separable across opponents' actions. If i's preferences satisfy a stronger version of this condition, then we can represent player i's preferences over all her actions using a utility that is additively separable across opponents. Our representation theorem thus identifies substantive restrictions on players' preferences implied by standard utilities for network games.