International Journal of Game Theory

, Volume 44, Issue 3, pp 599–629 | Cite as

Dynamic matching and bargaining with heterogeneous deadlines

  • Sjaak Hurkens
  • Nir Vulkan


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.


Bargaining Deadlines Markets 

JEL Classification

C73 C78 



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.


  1. Admati AR, Perry M (1987) Strategic delay in bargaining. Rev Econ Stud 54:345–364CrossRefGoogle Scholar
  2. Anwar AW, Sákovics J (2007) A decentralized market for a perishable good. B.E. J Theor Econ 7(1) (Contributions), Article 7Google Scholar
  3. Bester H, Sákovics J (2001) Delegated bargaining and renegotiation. J Econ Behav Organ 45:459–473CrossRefGoogle Scholar
  4. Bose G (1996) Bargaining economies with patient and impatient agents: equilibria and intermediation. Games Econ Behav 14:149–172CrossRefGoogle Scholar
  5. Burtraw D (1992) Strategic delegation in bargaining. Econ Lett 38:181–185CrossRefGoogle Scholar
  6. Cai H (2000) Bargaining on behalf of a constituency. J Econ Theory 92:234–273CrossRefGoogle Scholar
  7. Chavez A, Maes P (1996) Kasbah: an agent marketplace for buying and selling goods. In: Proceedings of the first international conference on the practical application of intelligent agents and multi-agent technology, London, April 1996Google Scholar
  8. Damiano E, Li H (2005) Unravelling of dynamic sorting. Rev Econ Stud 72:1057–1076CrossRefGoogle Scholar
  9. Duffie D, Gârleanu N, Pedersen LH (2005) Over-the-counter markets. Econometrica 73:1815–1847CrossRefGoogle Scholar
  10. Fershtman C, Seidmann D (1993) Deadline effects and inefficient delay in bargaining with endogenous commitment. J Econ Theory 60:306–321CrossRefGoogle Scholar
  11. Gale D (1987) Limit theorems for markets with sequential bargaining. J Econ Theory 43:20–54CrossRefGoogle Scholar
  12. Gale D (2000) Strategic foundations of general equilibrium: dynamic matching and bargaining games. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  13. Haller H, Holden S (1990) A letter to the editor on wage bargaining. J Econ Theory 52:232–236CrossRefGoogle Scholar
  14. Hurkens S, Vulkan N (2006) Dynamic matching and bargaining: the role of deadlines. Barcelona GSE Research Network WP, 188Google Scholar
  15. Jackson MO, Palfrey TR (1998) Efficiency and voluntary implementation in markets with repeated pairwise bargaining. Econometrica 66:1353–1388CrossRefGoogle Scholar
  16. Jennings NR, Faratin P, Johnson MJ, Norman TJ, O’Brien P, Wiegand ME (1996) Agent-based business process management. Int J Coop Inf Syst 5:105–130CrossRefGoogle Scholar
  17. Ma CA, Manove M (1993) Bargaining with deadlines and imperfect player control. Econometrica 61:1313–1339CrossRefGoogle Scholar
  18. Manea M (2012) Bargaining in dynamic markets with multiple populations. Mimeo, MITGoogle Scholar
  19. Merlo A, Ortalo-Magné F (2004) Bargaining over residential real estate: evidence from England. J Urban Econ 56:192–216CrossRefGoogle Scholar
  20. Merlo A, Wilson C (1995) A stochastic model of sequential bargaining with complete information. Econometrica 63:371–399CrossRefGoogle Scholar
  21. Mortensen DT, Wright R (2002) Competitive pricing and efficiency in search equilibrium. Int Econ Rev 43:1–20CrossRefGoogle Scholar
  22. Moreno D, Wooders J (2002) Prices, delay, and the dynamics of trade. J Econ Theory 104:304–339CrossRefGoogle Scholar
  23. Ponsati C (1995) The deadline effect: a theoretical note. Econ Lett 48:281–285CrossRefGoogle Scholar
  24. Rubinstein A (1982) Perfect equilibrium in a bargaining model. Econometrica 50:97–109CrossRefGoogle Scholar
  25. Rubinstein A, Wolinsky A (1985) Equilibrium in a market with sequential bargaining. Econometrica 53:1133–1150CrossRefGoogle Scholar
  26. Sákovics J (1993) Delay in bargaining games with complete information. J Econ Theory 59:78–95CrossRefGoogle Scholar
  27. Samuelson L (1992) Disagreement in markets with matching and bargaining. Rev Econ Stud 59:177–185CrossRefGoogle Scholar
  28. Sandholm T, Vulkan N (2000) Bargaining with deadlines. In: Proceedings of the national conference on artificial intelligence (AAAI), Orlando, FLGoogle Scholar
  29. Satterthwaite M, Shneyerov A (2007) Dynamic matching. Two-sided incomplete information, and participation costs: existence and convergence to perfect competition. Econometrica 75:155–200CrossRefGoogle Scholar
  30. Segendorff B (1998) Delegation and threat in bargaining. Games Econ Behav 23:266–283CrossRefGoogle Scholar
  31. Serrano R (2002) Decentralized information and the Walrasian outcome: a pairwise meetings market with private values. J Math Econ 38:65–89CrossRefGoogle Scholar
  32. Shimer R, Smith L (2000) Assortative matching and search. Econometrica 68:343–369CrossRefGoogle Scholar
  33. Shneyerov A, Wong A (2010a) The rate of convergence to perfect competition of matching and bargaining mechanisms. J Econ Theory 145:1164–1187CrossRefGoogle Scholar
  34. Shneyerov A, Wong A (2010b) Bilateral matching and bargaining with private information. Games Econ Behav 68:748–762CrossRefGoogle Scholar
  35. Sobel J, Takahashi I (1983) A multistage model of bargaining. Rev Econ Stud 50:411–426CrossRefGoogle Scholar
  36. Ståhl I (1972) Bargaining theory. Stockholm School of Economics, StockholmGoogle Scholar
  37. Vayanos D, Wang T (2007) Search and endogenous concentration of liquidity in asset markets. J Econ Theory 136:66–104CrossRefGoogle Scholar
  38. Yildiz M (2004) Optimism, deadline effect, and stochastic deadlines. Mimeo, MITGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institut d’Anàlisi Econòmica (CSIC) and Barcelona GSEBellaterraSpain
  2. 2.Saïd Business School and Worcester CollegeUniversity of OxfordOxfordUK

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