Advertisement

Beliefs, time and incomplete information in multiple encounter negotiations among autonomous agents

  • Sarit Kraus
Article

Abstract

In negotiations among autonomous agents over resource allocation, beliefs about opponents, and about opponents’ beliefs, become particularly important when there is incomplete information. This paper considers interactions among self‐motivated, rational, and autonomous agents, each with its own utility function, and each seeking to maximize its expected utility. The paper expands upon previous work and focuses on incomplete information and multiple encounters among the agents. It presents a strategic model that takes into consideration the passage of time during the negotiation and also includes belief systems. The paper provides strategies for a wide range of situations. The framework satisfies the following criteria: symmetrical distribution, simplicity, instantaneously, efficiency and stability.

Keywords

Incomplete Information Expected Utility Mixed Strategy Pure Strategy Belief Revision 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R.J. Aumann, Subjectivity and correlation in randomized strategies, Journal of Mathematical Economics 1(1) (1974) 67–96.MATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    L.M. Ausubel and R.J. Deneckere, Stationary sequential equilibria in bargaining with two sided incomplete information, Discussion Paper 784, Center for Mathematical Studies in Economics and Management Science, Northwestern University (1988).Google Scholar
  3. [3]
    F. Bacchus, A. Grove, J. Halpern and D. Koller, From statistics to beliefs, in: Proc. of AAAI-92 (California, 1992) pp. 602–608.Google Scholar
  4. [4]
    A.H. Bond and L. Gasser, An analysis of problems and research in DAI, in: Readings in Distributed Artificial Intelligence, eds. A.H. Bond and L. Gasser (Morgan-Kaufmann Publishers, Inc., San Mateo, California, 1988) pp. 3–35.Google Scholar
  5. [5]
    E. Bond and L. Samuelson, Durable good monopolies with rational expectation and replacement sales, Rand Journal of Economics 15 (1984) 336–345.MathSciNetCrossRefGoogle Scholar
  6. [6]
    E. Bond and L. Samuelson, The Coase conjecture need not hold for durable good monopolies with depreciation, Economics Letters 24 (1987) 93–97.MathSciNetCrossRefGoogle Scholar
  7. [7]
    N. Carver, Z. Cvetanovic and V. Lesser, Sophisticated cooperation in FA/C distributed problem solving systems, in: Proc. of AAAI-91 (California, 1991) pp. 191–198.Google Scholar
  8. [8]
    K. Chatterjee and L. Samuelson, Bargaining with two-sided incomplete information: An infinite horizon model with alternating offers, Review of Economic Studies 54 (1987) 175–192.MATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    I.K. Cho, Characterization of stationary equilibria in bargaining models with incomplete information, Unpublished paper, Department of Economics, University of Chicago (1989).Google Scholar
  10. [10]
    P. Cohen and H. Levesque, Teamwork, Noûs (1991) 487–512.Google Scholar
  11. [11]
    S.E. Conry, R.A. Meyer and V.R. Lesser, Multi-stage negotiation in distributed planning, in: Readings in Distributed Artificial Intelligence, eds. A.H. Bond and L. Gasser (Morgan-Kaufmann Publishers, Inc., San Mateo, California, 1988) pp. 367–384.Google Scholar
  12. [12]
    S.E. Conry, K. Kuwabara, V.R. Lesser and R.A. Meyer, Multi-stage negotiation for distributed satisfaction, IEEE Transactions on Systems, Man, and Cybernetics, Special Issue on Distributed Artificial Intelligence 21(6) (December 1991) 1462–1477.MATHGoogle Scholar
  13. [13]
    K. Decker and V. Lesser, A one-shot dynamic coordination algorithm for distributed sensor networks, in: Proc. of AAAI-93 (1993) pp. 210–216.Google Scholar
  14. [14]
    J. Doyle, Some theories of reasoned assumptions: an essay in rational psychology, Technical Report 83-125, Department of Computer Science, Carnegie Mellon University, Pittsburgh, PA (1983).Google Scholar
  15. [15]
    J. Doyle, Rational belief revision, Technical Report, MIT, Artificial Intelligence Laboratory, Cambridge, Massachusettes (1990). Unpublished paper.Google Scholar
  16. [16]
    D. Dubois and H. Prade, A survey of belief revision and updating rules in various uncertainty models, International Journal of Intelligent Systems 9 (1994) 61–100.MATHMathSciNetGoogle Scholar
  17. [17]
    E.H. Durfee, Coordination of Distributed Problem Solvers (Kluwer Academic Publishers, Boston, 1988).Google Scholar
  18. [18]
    E. Ephrati and J.S. Rosenschein, The Clarke Tax as a consensus mechanism among automated agents, in: Proc. of AAAI-91 (California, 1991) pp. 173–178.Google Scholar
  19. [19]
    E. Ephrati and J.S. Rosenschein, Reaching agreement through partial revelation of preferences, in: Proceedings of the Tenth European Conference on Artificial Intelligence, Vienna, Austria (August 1992) pp. 229–233.Google Scholar
  20. [20]
    R. Fagin, G. Kuper, J. Ullman and M. Vardi, Updating logical databases, in: Advances in Computing Research, Vol. 3 (1986) pp. 1–18.Google Scholar
  21. [21]
    D. Fudenberg and J. Tirole, Game Theory, Chapter 8 (MIT Press, Cambridge, MA, 1991).Google Scholar
  22. [22]
    P. Gardenfors, Knowledge in Flux: Modeling the Dynamics of Epistemic States (MIT Press, 1988).Google Scholar
  23. [23]
    J.Y. Halpern and Y. Moses, Knowledge and common knowledge in a distributed environment, Journal of the Association for Computing Machinery 37(3) (1990).Google Scholar
  24. [24]
    G. Harman, Change in View (MIT Press, Cambridge, MA, 1986).Google Scholar
  25. [25]
    W.L. Harper, Rational belief change, popper functions, and counterfactuals, in: Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. 1, eds. W.L. Harper and C.A. Hooker (Reidel, Dordrecht, 1976) pp. 73–115.Google Scholar
  26. [26]
    O.D. Hart and J. Tirole, Contract renegotiation and Coasian dynamics, Review of Economic Studies (1988) pp. 509–540.Google Scholar
  27. [27]
    H. Katsuno and A. Mendelzon, Knowledge base revision and minimal change, Artificial Intelligence 52 (1991) 263–294.MATHMathSciNetCrossRefGoogle Scholar
  28. [28]
    H. Katsuno and A. Mendelzon, On the difference between updating a knowledge base and revising it, in: Proc. of KR91 (1991) pp. 387–394.Google Scholar
  29. [29]
    S. Kraus and D. Lehmann, Knowledge, belief and time, Theoretical Computer Science 58 (1988) 155–174.MATHMathSciNetCrossRefGoogle Scholar
  30. [30]
    S. Kraus and D. Lehmann, Designing and building a negotiating automated agent, Computational Intelligence 11(1) (1995) 132–171.Google Scholar
  31. [31]
    S. Kraus and J. Wilkenfeld, The function of time in cooperative negotiations, in: Proc. of AAAI-91 (California, 1991) pp. 179–184.Google Scholar
  32. [32]
    S. Kraus and J. Wilkenfeld, Negotiations over time in a multi-agent environment: Preliminary report, in: Proc. of IJCAI-91 (Australia, 1991) pp. 56–61.Google Scholar
  33. [33]
    S. Kraus and J. Wilkenfeld, A strategic negotiations model with applications to an international crisis, IEEE Transaction on Systems Man and Cybernetics 23(1) (1993) 313–323.MATHCrossRefGoogle Scholar
  34. [34]
    S. Kraus, J. Wilkenfeld and G. Zlotkin, Multi-agent negotiation under time constraints, Artificial Intelligence 75(2) (1995) 297–345.MATHMathSciNetCrossRefGoogle Scholar
  35. [35]
    D. Kreps and R. Wilson, Reputation and imperfect information, Journal of Economic Theory 27 (1982) 253–279.MATHMathSciNetCrossRefGoogle Scholar
  36. [36]
    D. Kreps and R. Wilson, Sequential equilibria, Econometrica 50 (1982) 863–894.MATHMathSciNetCrossRefGoogle Scholar
  37. [37]
    K. Kuwabara and V. Lesser, Extended protocol for multi-stage negotiation, in: Proc. of the Ninth Workshop on Distributed Artificiall Intelligence (1989) pp. 129–161.Google Scholar
  38. [38]
    B. Laasri, H. Laasri and V. Lesser, A generic model for intelligent negotiating agents, International Journal on Intelligent Cooperative Information Systems 1(2) (1992) 291–317.CrossRefGoogle Scholar
  39. [39]
    G. Lemel, A strategic model for negotiation among autonomous agents, M.Sc. Thesis, Dept. of Mathematics and Computer Science, Bar-Ilan University, Ramat Gan (written largely in Hebrew) (1995).Google Scholar
  40. [40]
    V.R. Lesser, J. Pavlin and E.H. Durfee, Approximate processing in real time problem solving, AI Magazine 9(1) (1988) 49–61.Google Scholar
  41. [41]
    V.R. Lesser, A retrospective view of FA/C distributed problem solving, IEEE Transactions on Systems, Man, and Cybernetics 21(6) (1991) 1347–1362.CrossRefGoogle Scholar
  42. [42]
    D. Lewis, Counterfactuals (Blackwell, Oxford, 1973).Google Scholar
  43. [43]
    R.D. Luce and H. Raiffa, Games and Decisions (John Wiley and Sons, 1957).Google Scholar
  44. [44]
    V. Madrigal, T. Tan and R. Werlang, Support restrictions and sequential equililibria, Journal of Economic Theory 43 (1987) 329–334.MATHCrossRefGoogle Scholar
  45. [45]
    T.W. Malone, R.E. Fikes, K.R. Grant and M.T. Howard, Enterprise: A market-like task schedule for distributed computing environments, in: The Ecology of Computation, ed. B.A. Huberman (North-Holland, 1988) pp. 177–205.Google Scholar
  46. [46]
    P. Milgrom and J. Roberts, Predation, reputation, and entry deterrence, Journal of Economic Theory 27 (1982) 280–312.MATHMathSciNetCrossRefGoogle Scholar
  47. [47]
    T. Moehlman, V. Lesser and B. Buteau, Decentralized negotiation: An approach to the distributed planning problem, Group Decision and Negotiation 2 (1992) 161–191.CrossRefGoogle Scholar
  48. [48]
    M.J. Osborne and A. Rubinstein, Bargaining and Markets (Academic Press Inc., San Diego, California, 1990).Google Scholar
  49. [49]
    W.V. Quine and J.S. Ullian, The Web of Belief, 2nd edn. (Random House, New York, 1978).Google Scholar
  50. [50]
    A.S. Rao and N.Y. Foo, Formal theories of belief revision, in: Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning (Morgan-Kaufmann, May 1989) pp. 369–380.Google Scholar
  51. [51]
    E. Rasmusen, Games and Information (Basil Blackwell Ltd., Cambridge, MA, 1989).Google Scholar
  52. [52]
    J.S. Rosenschein, Rational interaction: cooperation among intelligent agents, PhD Thesis, Stanford University (1986).Google Scholar
  53. [53]
    J.S. Rosenschein and G. Zlotkin, Rules of Encounter: Designing Conventions for Automated Negotiation Among Computers (MIT Press, Boston, 1994).Google Scholar
  54. [54]
    A. Rubinstein, Perfect equilibrium in a bargaining model, Econometrica 50(1) (1982) 97–109.MATHMathSciNetCrossRefGoogle Scholar
  55. [55]
    A. Rubinstein, A bargaining model with incomplete information about preferences, Econometrica 53(5) (1985) 1151–1172.MATHMathSciNetCrossRefGoogle Scholar
  56. [56]
    T. Sandholm, An implementation of the contract net protocol based on marginal cost calculations, in: Proc. of AAAI-93 (1993) pp. 256–262.Google Scholar
  57. [57]
    L.J. Savage, The Foundations of Statistics, 2nd edn. (Dover Publications, New York, 1972).Google Scholar
  58. [58]
    R.G. Smith and R. Davis, Negotiation as a metaphor for distributed problem solving, Artificial Intelligence 20 (1983) 63–109.CrossRefGoogle Scholar
  59. [59]
    W. Spivey and R. Thrall, Linear Optimization (Holt, Rinehart and Winston, 1970).Google Scholar
  60. [60]
    R.C. Stalnaker, Inquiry (MIT Press, Cambridge, MA, 1984).Google Scholar
  61. [61]
    K.P. Sycara, Persuasive argumentation in negotiation, Theory and Decision 28 (1990) 203–242.CrossRefGoogle Scholar
  62. [62]
    K.P. Sycara, Resolving adversarial conflicts: an approach to integrating case-based and analytic methods, PhD Thesis, School of Information and Computer Science, Georgia Institute of Technology (1987).Google Scholar
  63. [63]
    M. Wellman, A general-equilibrium approach to distributed transportation planning, in: Proc. of AAAI-92 (San Jose, California, 1992) pp. 282–289.Google Scholar
  64. [64]
    M. Winslett, Is belief revision harder than you thought?, in: Proceedings of AAAI-86 (Philadelphia, 1986) pp. 421–427.Google Scholar
  65. [65]
    G. Zlotkin and J.S. Rosenschein, Cooperation and conflict resolution via negotiation among autonomous agents in noncooperative domains, IEEE Transactions on Systems, Man, and Cybernetics, Special Issue on Distributed Artificial Intelligence 21(6) (December 1991) 1317–1324.MATHGoogle Scholar
  66. [66]
    G. Zlotkin and J.S. Rosenschein, Incomplete information and deception in multi-agent negotiation, in: Proc. IJCAI-91 (Australia, 1991) pp. 225–231.Google Scholar
  67. [67]
    G. Zlotkin and J.S. Rosenschein, A domain theory for task oriented negotiation, in: Proceedings of IJCAI-93 (Chambery, France, August 1993) pp. 416–422.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Sarit Kraus
    • 1
    • 2
  1. 1.Department of Mathematics and Computer ScienceBar Ilan UniversityRamat GanIsrael
  2. 2.Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA

Personalised recommendations