Uncertainty and Delay in Bargaining

Strategic Delay in Bargaining with Two-Sided Uncertainty

“…In particular, when stationarity is relaxed, then the game with one-sided offers has an equilibrium that yields the ex ante efficient payoffs in the limit as the time between offers goes to zero. In stark contrast, the equilibria identified in the one-sided-offer models of Cramton (1984a) and Cho (1990b) have the property that if the valuation distributions for the seller and the buyer completely overlap, then in the limit as the time between offers goes to zero, the expected gains realized in equilibrium go to zero. All the gains from trade are consumed by delay of infinite duration.…”

“…(Ausubel and Deneckere (1991) prove this "no trade" result more generally.) An implication of the "no trade," result is that the equilibrium payoffs in Cramton (1984a) and Cho (1990b) are quite sensitive to the time between offers. Whether the bargainers can make offers once a day, once an hour, or once a minute has a first-order affect on their payoffs.…”

“…The importance of analyzing this case rests on the premise that bargainers typically are uncertainty about each others' reservation values. A second premise is that bargaining is more realistically modelled by alternating offers; whereas, most studies of bargaining with two-sided uncertainty allow only one party to make offers Deneckere (1988, 1991), Cho (1990b), and Cramton (1984a)). This paper differs from two other papers that allow alternating offers in a setting of two-sided uncertainty.…”

Mediation: incomplete information bargaining with filtered communication

“…Apart from the fact that this is a more realistic scenario -the existence of a smallest money unit and the non-existence 3 See Ponsatí and Sákovics (1995). 4 See Fudenberg and Tirole (1983), Cramton (1984Cramton ( ,1992, Chatterjee and Samuelson (1987), Cho (1990), Deneckere (1992b,1993), Ponsati (1997) and Watson (1998) for some valuable partial results.…”

“…The first derivative of the objective function can be written as (we suppress the dependence on time for simplicity) e −z1 t A, where A is the LHS of equation (11). Consequently, the second derivative has the form −z 1 e −z1t A + e −z1t dA dt Thus, since A is zero at the singular point, we only need to prove that dA dt is negative.…”