Dynamic Matching and Bargaining with heterogeneous Deadlines

Sjaak Hurkens and Nir Vulkan

Abstract: This paper analyzes bargaining outcomes when agents do not have stationary time preferences (as represented by a constant discount factor) but are pressed by rm deadlines. We consider a dynamic model where traders with heterogeneous deadlines are matched randomly into pairs who then bargain about the division of a xed surplus. A trader leaves the market when an agreement has been reached or when his deadline expires. Our analysis encompasses both the case of perfect and imperfect information about the partner's deadline. We define, characterize and show the existence of a stationary equilibrium configuration. We characterize when delay occurs and when deadlines are missed in equilibrium and show that the payoffs of traders are strictly increasing and concave in own deadline, unless bargaining takes place under imperfect information and no delay occurs, in which case all pairs immediately agree on an almost even split. We provide comparative statics exercises and illustrate our results by some examples.

Key Words: Bargaining, deadlines, markets.

Classification Number: C73; C78.

International Journal of Game Theory. Forthcoming