Dynamic matching and bargaining with heterogeneous

Authors: Sjaak Hurkens Nir Vulkan

Publish Date: 2014/08/27

Volume: 44, Issue: 3, Pages: 599-629

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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 examplesHurkens gratefully acknowledges financial support from the Spanish Ministry of Economy and Competitiveness through grant ECO201237065 from AGAUR through grant 2014SGR510 and through the Severo Ochoa Programme for Centres of Excellence in RD SEV20110075 We thank the editor two anonymous referees Yossi Feinberg Zvika Neeman Larry Samuelson and various seminar audiences for helpful commentsWe first show that w i is increasing in i Obviously 0=w 0 w 1 Assume that w 0 w 1 cdots w i for some ige 1 It is immediate that then w i+1w i because by the induction step w i w i1 and max delta w i 1delta w j1 ge max delta w i1 1delta w j1 for all j

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