Skip to main content
Log in

Bargaining with incomplete information

  • Published:
Annals of Mathematics and Artificial Intelligence Aims and scope Submit manuscript

Abstract

This paper analyses the process and outcomes of competitive bilateral negotiation for a model based on negotiation decision functions. Each agent has time constraints in the form of a deadline and a discounting factor. The importance of information possessed by participants is highlighted by exploring all possible incomplete information scenarios – both symmetric and asymmetric. In particular, we examine a range of negotiation scenarios in which the amount of information that agents have about their opponent’s parameters is systematically varied. For each scenario, we determine the equilibrium solution and study its properties. The main results of our study are as follows. Firstly, in some scenarios agreement takes place at the earlier deadline, while in others it takes place near the beginning of negotiation. Secondly, in some scenarios the price surplus is split equally between the agents while in others the entire price surplus goes to a single agent. Thirdly, for each possible scenario, the equilibrium outcome possesses the properties of uniqueness and symmetry – although it is not always Pareto optimal. Finally, we also show the relative impacts of the opponent’s parameters on the bargaining outcome.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P. Faratin, C. Sierra and N.R. Jennings, Negotiation decision functions for autonomous agents, International Journal of Robotics and Autonomous Systems 24(3–4) (1998) 159–182.

    Article  Google Scholar 

  2. S.S. Fatima, M. Wooldridge and N.R. Jennings, The influence of information on negotiation equilibrium, in: Agent Mediated Electronic Commerce IV, Designing Mechanisms and Systems, eds. J. Padget, O. Shehory, D. Parkes, N. Sadeh and W.E. Walsh (Springer-Verlag, 2002) pp. 180–193.

  3. S.S. Fatima, M. Wooldridge and N.R. Jennings, Multi-issue negotiation under time constraints, in: Proceedings of the First International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS-02). Bologna, Italy (2002) pp. 143–150.

  4. S.S. Fatima, M. Wooldridge and N.R. Jennings, Optimal negotiation strategies for agents with incomplete information, in: Intelligent Agents VIII. Agent Theories, Architectures and Languages, eds. J.J. Meyer and M. Tambe (Springer-Verlag, 2002) pp. 377–392.

  5. S.S. Fatima, M. Wooldridge and N.R. Jennings, An agenda based framework for multi-issue negotiation, Artificial Intelligence Journal (to appear).

  6. C. Fershtman and D.J. Seidmann, Deadline effects and inefficient delay in bargaining with endogenous commitment, Journal of Economic Theory 60(2) (1993) 306–321.

    Article  Google Scholar 

  7. D. Fudenberg, D. Levine and J. Tirole, Infinite horizon models of bargaining with one sided incomplete information, in: Game Theoretic Models of Bargaining, ed. A. Roth (University of Cambridge Press, Cambridge, 1985).

    Google Scholar 

  8. D. Fudenberg and J. Tirole, Sequential bargaining with incomplete information, Review of Economic Studies 50 (1983) 221–247.

    Google Scholar 

  9. J. Harsanyi and R. Selten, A generalized Nash solution for two-person bargaining games with incomplete information, Management Science 18(5) (1972) 80–106.

    Google Scholar 

  10. J.C. Harsanyi, Approaches to the bargaining problem before and after the theory of games, Econometrica 24 (1956) 144–157.

    Google Scholar 

  11. N.R. Jennings, P. Faratin, A.R. Lomuscio, S. Parsons and M. Wooldridge, Automated negotiation: Prospects, methods and challenges, Group Decision and Negotiation 10(2) (2001) 199–215.

    Article  Google Scholar 

  12. N.R. Jennings, P. Faratin, T.J. Norman, P. O’Brien, B. Odgers and J.L. Atly, Implementing a business process management system using adept: A real-world case study, Int. Journal of Applied Artificial Intelligence 14(5) (2000) 421–463.

    Article  Google Scholar 

  13. R. Keeney and H. Raiffa, Decisions with Multiple Objectives: Preferences and Value Tradeoffs (Wiley, New York, 1976).

    Google Scholar 

  14. S. Kraus, Strategic Negotiation in Multi-Agent Environments (The MIT Press, Cambridge, MA, 2001).

    Google Scholar 

  15. D.M. Kreps and R. Wilson, Sequential equilibrium, Econometrica 50 (1982) 863–894.

    Google Scholar 

  16. A. Lomuscio, M. Wooldridge and N.R. Jennings, A classification scheme for negotiation in electronic commerce, International Journal of Group Decision and Negotiation 12(1) (2003) 31–56.

    Article  Google Scholar 

  17. C.A. Ma and M. Manove, Bargaining with deadlines and imperfect player control, Econometrica 61 (1993) 1313–1339.

    Google Scholar 

  18. J.F. Nash, The bargaining problem, Econometrica 18 (1950) 155–162.

    Google Scholar 

  19. M.J. Osborne and A. Rubinstein, A Course in Game Theory (The MIT Press, 1994).

  20. D.G. Pruitt, Negotiation Behavior (Academic Press, 1981).

  21. H. Raiffa, The Art and Science of Negotiation (Harvard University Press, Cambridge, 1982).

    Google Scholar 

  22. J.S. Rosenschein and G. Zlotkin, Rules of Encounter (MIT Press, 1994).

  23. A. Rubinstein, Perfect equilibrium in a bargaining model, Econometrica 50(1) (1982) 97–109.

    Google Scholar 

  24. A. Rubinstein, A bargaining model with incomplete information about time preferences, Econometrica 53 (1985) 1151–1172.

    Google Scholar 

  25. T. Sandholm, Agents in electronic commerce: component technologies for automated negotiation and coalition formation, Autonomous Agents and Multi-Agent Systems 3(1) (2000) 73–96.

    Article  Google Scholar 

  26. T. Sandholm and N. Vulkan, Bargaining with deadlines, in: AAAI-99, Orlando, FL (1999) pp. 44–51.

  27. E. VanDamme, Refinements of the Nash Equilibrium Concept (Springer-Verlag, Berlin, 1983).

    Google Scholar 

  28. O.R. Young, Bargaining: Formal Theories of Negotiation (University of Illinois Press, Urbana, 1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shaheen S. Fatima.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fatima, S.S., Wooldridge, M. & Jennings, N.R. Bargaining with incomplete information. Ann Math Artif Intell 44, 207–232 (2005). https://doi.org/10.1007/s10472-005-4688-7

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10472-005-4688-7

Keywords

Navigation