A Contraction Principle for Finite Global Games

I provide a new proof of uniqueness of equilibrium in a wide class of global games. I show that the joint best-response in these games is a contraction. The uniqueness result then follows as a corollary of the contraction property. Furthermore, the contraction mapping approach provides a revealing intuition for why uniqueness arises: Complementarities in games generate multiplicity of equilibria, but the global games structure dampens complementarities so that only one equilibrium exists. I apply my result to show that uniqueness is obtained through contraction in currency crises and Diamond's search models.