Symmetries in Network Games

Who counts as "the same" in a network, and when must they act or be treated identically? Whilst many economic settings are network games, where with whom agents interact shapes their behaviour, this question has remained largely unanswered. I develop a general notion of identical network incentives and use it to organise the analysis of equilibria and interventions in network games. I introduce algebraic tools that leverage network symmetries, which fold the network so that nodes on either side of the fold occupy identical positions. In unique or extremal equilibria, agents with the same network position must take the same action. These equilibria can admit tractable comparative statics. For budget-constrained interventions, symmetries structure how changes in incentives flow through the network, revealing a contrast as the budget grows. With complements in the network externality, total good provision shifts by the same amount amongst similar agents. With substitutes, targeting can fix total good provision by simply redistributing the original total equilibrium action amongst equivalent agents.