Global Games

Abstract

Complete information games often have multiple Nash equilibria. Game theorists have long been interested in finding a way of removing or reducing that multiplicity. Carlsson and van Damme (1993) (CvD) introduced an original and attractive approach to doing so. A complete information model entails the implicit assumption that there is common knowledge among the players of the payoffs of the game. In practice, such common knowledge will often be lacking. CvD suggested a convenient and intuitive way of relaxing that common knowledge assumption: suppose that, instead of observing payoffs exactly, payoffs are observed with a small amount of continuous noise; and suppose that — before observing their signals of payoffs — there was an ex ante stage where any payoffs were possible. Based on the latter feature, CvD dubbed such games ‘global games’. It turns out that there is a unique equilibrium in the game with a small amount of noise. This uniqueness remains no matter how small the noise is and is independent of the distribution of the noise. Since complete information, or common knowledge of payoffs, is surely always an idealization anyway, the play selected in the global game with small noise can be seen as a prediction for play in the underlying complete information game.