Without assuming rational expectations, the author examines the implications of a stationarity assumption in a standard bargaining model with one-sided incomplete information, where the seller makes an offer in each period. Instead of computing a weakly stationary equilibrium, the author invokes rationalizability combined with the restriction that the buyer's acceptance rule be weakly stationary. There exists a pair of rationalizable sets of pure strategies for the seller and the buyer that are weakly stationary. The author demonstrates that any initial offer from the seller induced by a strategy rationalized by a weakly stationary acceptance rule for the buyer must entail the Coase property. Copyright 1994 by The Review of Economic Studies Limited.

This paper studies the following problem. An agent takes actions based on a possibly misspecified model. The agent is large, in the sense that his actions influence the model he is trying to learn about. The agent is aware of potential model misspecification and tries to detect it, in real-time, using an econometric specification test. If his model fails the test, he formulates a new better-fitting model. If his model passes the test, he uses it to formulate and implement a policy based on the provisional assumption that the current model is correctly specified, and will not change in the future. We claim that this testing and model validation process is an accurate description of most macroeconomic policy problems. Unfortunately, the dynamics produced by this process are not at all well understood. We make progress on this problem by relating it to a problem that is well understood. In particular, we relate it to the dynamics of constant-gain stochastic approximation algorithms. Doing this enables us to appeal to well known results from the large deviations literature to help us understand the dynamics of testing and model revision. We show that as the agent applies an increasingly stringent specification test, the large deviation properties of the discrete model validation dynamics converge to those of the continuous learning dynamics. This sheds new light on the recent constant-gain learning literature. JEL Classification Numbers: C120, E590 1.