This paper investigates the relationship between uncertainty and delay of agreement in the one-sided offer bargaining model with two-sided uncertainty where the seller makes offers. We construct a weak stationary equilibrium in which different types of the seller charge different prices in every period. We completely characterize the separating equilibrium by three regularity conditions, and show that the time interval between offers converges to zero, the seller's initial price offer in a separating equilibrium converges with probability 1 to the lowest valuation of the buyer if and only if the gain from trading is common knowledge.

This paper proves that the monotonicity of bidding strategies together with the rationality of bidders implies that the winning bid in a first price auction converges to the competitive equilibrium price as the number of bidders increases (Wilson (1977)). Instead of analyzing the symmetric Nash equilibrium, we examine rationalizable strategies (Bernheim (1984) and Pearce (1984)) among the set of monotonic bidding strategies to prove that any monotonic rationalizable bidding strategy must be within a small neighborhood of the “true ” valuation of the object, conditioned on the signal received by the bidder. We obtain an information aggregation result similar to Wilson (1977), while dispensing with almost all symmetric assumptions and using a milder solution concept than the Nash equilibrium. In particular, if every bidder is ex ante identical, then any rationalizable bidding strategy must be within a small neighborhood of the symmetric Nash equilibrium. In a symmetric first price auction, the symmetry of outcomes is implied rather than assumed.