On Dynamic Adjustment and Comparative Statics Via the Implicit Function Theorem

The implicit function theorem (IFT) offers a way of deriving a correspondence between the parameter space and the Nash equilibria of a game. However, which equilibrium will actually emerge after a parameter change involves a dynamic adjustment process, which may significantly differ from IFT predictions. Utilizing the notion of local uniform contraction mappings, we show that IFT predictions are consistent with economic behavior at locally contraction stable equilibria, which is both a necessary and sufficient condition in games of strategic complements. When best response functions are monotone, we can address the convergence of play under more general adaptive dynamics.