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.