# Dynamic matching and bargaining with heterogeneous deadlines

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## 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 firm deadlines. We consider a dynamic model where traders with heterogeneous deadlines are matched randomly into pairs who then bargain about the division of a fixed 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.

## Keywords

Bargaining Deadlines Markets## JEL Classification

C73 C78## Notes

### Acknowledgments

Hurkens gratefully acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through grant ECO2012-37065, from AGAUR through grant 2014SGR510 and through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2011-0075). We thank the editor, two anonymous referees, Yossi Feinberg, Zvika Neeman, Larry Samuelson and various seminar audiences for helpful comments.

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