Fully Aggregative Games

We study aggregative games in which players ’ strategy sets are convex intervals of the real line and (not necessarily differentiable) payoffs depend only on a player’s own strategy and the sum of all players ’ strategies. We give sufficient conditions on each player’s pay-off function to ensure the existence of a unique Nash equilibrium in pure strategies, emphasizing the geometric nature of these conditions. These conditions are almost best possible in the sense that the re-quirements on one player can be slightly weakened, but any further weakening may lead to multiple equilibria. The same conditions also permit the analysis of comparative statics and the competitive limit. We discuss the application of these conditions in a range of examples, chosen to illustrate various aspects their use. We also show that all restrictions on payoffs in aggregative games that guarantee the exis-tence of a unique equilibrium of which we are aware are covered b