Structural Stability Implies Robustness to Bounded Rationality

The introduction of a small amount of bounded rationality into a model sometimes has little effect, and sometimes has a dramatic impact on predicted behavior. We call a model robust to bounded rationality if small deviations from rationality result only in small changes in the equilibrium set. We also say that a model is structurally stable if the equilibrium set (given fully rational agents) varies continuously with the parameter values of the model. It is easy to see that when the equilibrium set is discontinuous, bounded rationality can have a very large impact on behavior in the neighborhood of the discontinuity. We go further and show that it is only at such discontinuities that bounded rationality can have large effects. It follows that a model is robust to bounded rationality if and only if it is structurally stable. Thus, we can characterize which models will be robust to bounded rationality and which will not, independently of the exact form that the bounded rationality takes. Journal of Economic Literature Classification Numbers: C69, C79, D51, E19.