Stationarity, rationalizability and bargaining

Without assuming rational expectations, we examine 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, we invoke rationalizability (Bernheim (1984) and Pearce (1984)) 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 which are weakly stationary. We demonstrate 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. Our result does not presume the selection of a particular equilibrium and follows directly from the weak stationarity assumption of the buyer’s acceptance rule and the rational behaviour of the players.