A model of noisy introspection

We present a theoretical model of noisy introspection designed to explain behavior in games played only once. The model determines layers of beliefs about others' beliefs about …, etc., but allows for surprises by relaxing the equilibrium requirement that belief distributions coincide with decision distributions. Noise is injected into iterated conjectures about others' decisions and beliefs, which causes the predictions to differ from those of deterministic models of iterated thinking, e.g., rationalizability. The paper contains a convergence proof that implies existence and uniqueness of the outcome of the iterated thought process. In addition, estimated introspection and noise parameters for data from 37 one-shot matrix games are reported. The accuracy of the model is compared with that of several alternatives.