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Bargaining with Deadlines and Imperfect Player Control

Ching-to Albert Ma
Michael Manove

Abstract

Anecdotal and experimental evidence suggests that bargaining sessions subject to deadlines often begin with cheap talk and rejected proposals. Agreements, if they are reached at all, tend to be concluded near the deadline. We attempt to capture and explain these phenomena in a strategic bargaining model that incorporates a bargaining deadline, the possibility of strategic delay, and a lack of perfect player control over the timing of offers. Imperfect player control is generated by an exogenous uniformly-distributed random delay in offer transmission. Our model has a symmetric Markov-perfect equilibrium, unique at almost all nodes, in which players adopt strategic delay early in the game, make and reject offers later on, and reach agreements late in the game if at all. In equilibrium players miss the deadline with positive probability. The expected division of the surplus is unique and close to an even split.