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.

The author proposes a refinement of seq uential equilibrium for extensive form games by generalizing a restri ction proposed for signaling games in Cho and D. M. Kreps (1987). The restriction is that beliefs must not assign positive weight to the p ossibilities that can be excluded through reasonable introspection ba sed on the data available as common knowledge. A new technique is dev eloped in order to prove the existence of forward induction equilibri um, which consists of two steps. First, the author establishes the ge neric existence of forward induction equilibrium by exploiting the re sults of E. Kohlberg and J. F. Mertens (1986). Then, he shows that th e forward induction equilibrium correspondence is upper hemicontinuou s in the outcome space with respect to the changes of parameters of t he game. Copyright 1987 by The Econometric Society.

ABSTRACT. 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.

Games in which one party conveys private information to a second through messages typically admit large numbers of sequential equilibria, as the second party may entertain a wealth of beliefs in response to out-of-equilibrium messages. By restricting those out-of-equilibrium beliefs, one can sometimes eliminate many unintuitive equilibria. We present a number of formal restrictions of this sort, investigate their behavior in specific examples, and relate these restrictions to Kohlberg and Mertens' notion of stability.