Characterising equilibrium selection in global games with strategic complementarities

Global games are widely used for equilibrium selection to predict behaviour in complete information games with strategic complementarities. We establish two results on the global game selection. First, we show that it is independent of the payoff functions of the global game embedding, though it may depend on the noise distribution. Second, we give a simple sufficient criterion for noise independence in many action games. A many action game may be noise independent if it can be suitably decomposed into smaller (say, binary action) games, for which there are simple criteria guaranteeing noise independence. We delineate the games where noise independence may be established by counting the number of players or actions. In addition, we give an elementary proof that robustness to incomplete information implies noise independence.