Bargaining and Waiting

Abstract

Until recently the final word on bargaining with full information had been Rubinstein's (1982) seminal work which concluded that an agreement will be reached immediately, and the first mover will have the advantageous share. Rubinstein's model was one of alternating offers made at fixed time intervals. Many variations of the model have emerged, and until recently, they mainly focus on asymmetric information' with some having the uninformed agent making all the offers. The conclusion from examining these variations is that the equilibrium is highly sensitive to the exact specification of the institutional structure. In more recent work, Perry and Reny (1990), Perry and Reny (1993), Sakavics (1993), and Nickerson, Sadanand and Sadanand (1994) endogenize the structure of the bargaining by allowing the order and timing of play to be determined endogenously. The first three papers (endogenous structure models) deal with the full information setting and the last is an asymmetric information model.2 In addition to the exogenously given minimum reaction time (for responding to offers made by the other player), the endogenous structure models introduce the important innovation of an exogenous waiting time, a time between a player's offer and his next offer. They also allow players to make simultaneous offers which Sakovics later disallows. The findings in this recent literature are rather startling: (i) The waiting time has a profound impact; the longer the time, the greater the share the player can command.3 (ii) The consequence of simultaneous offers is multiple equilibria: when the reaction time is zero, a continuum of shares lying between the two unique Rubinstein shares can result, and additional continua of shares arise with delayed agreement when the reaction times are positive. (iii) Equilibrium paths are almost exclusively characterized by simultaneous offers. In this paper we examine the question of simultaneous offers and reconcile the conflict between the infrequency of simultaneous offers in real life bargaining and their prevalence in the endogenous structure models. We