A Fuzzy Game Theoretic Approach to Multi-Agent Coordination

  • Shih-Hung Wu
  • Von-Wun Soo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1599)


Game theoretic decision making is a practical approach to multi-agent coordination. Rational agents may make decisions based on different principles of rationality assumptions that usually involve knowledge of how other agents might move. After formulating a game matrix of utility entries of possible combination of moves from both agents, agents can reason which combination is the equilibrium. Most previous game theoretic works treat the utility values qualitatively (i.e., consider only the order of the utility values). This is not practical since the utility values are usually approximate and the differences between utility values are somewhat vague. In this paper, we present a fuzzy game theoretic decision making mechanism that can deal with uncertain utilities. We thus construct a fuzzy-theoretic game framework under both the fuzzy theory and the game theory. The notions of fuzzy dominant relations, fuzzy Nash equilibrium, and fuzzy strategies are defined and fuzzy reasoning are carried out in agent decision making. We show that a fuzzy strategy can perform better than a mixed strategy in traditional game theory in dealing with more than one Nash equilibrium games.


Nash Equilibrium Fuzzy Number Mixed Strategy Dominant Strategy Strategy Combination 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aubin, J. P.: Fuzzy core and equilibrium of games defined in strategic form. In: Ho, Y.C., Mitter, S.K.(eds.): Directions in Large-Scale Systems, Plenum, New York(1976)371–388Google Scholar
  2. 2.
    Bellman, R.E., Zadeh, L.A.: Decision Making in a Fuzzy Environment. Management Sci. Vol.17(1970)141–164MathSciNetGoogle Scholar
  3. 3.
    Brafman, R., Tennenholtz, M.: On the Foundations of Qualitative Decision Theory, In: Proceedings of the National Conference on Artificial Intelligence, Portland, OR(1996)Google Scholar
  4. 4.
    Brams, S.J.: Theory of Moves, American Scientist Vol.81(1993)562–570Google Scholar
  5. 5.
    Butnariu, D.: Fuzzy Games: A Description of the Concept. Fuzzy Sets and Systems Vol.1(3), (1978)181–192zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York(1980)zbMATHGoogle Scholar
  7. 7.
    Genesereth, M.R., Ginsberg, M.L., Rosenschein, J. S.: Cooperation without Communication. In: Proceedings of the National Conference on Artificial Intelligence. Philadelphia, Pennsylvania (1986)51–57Google Scholar
  8. 8.
    Mor, Y., Rosenschein, J.S.: Time and the Prisoner’s Dilemma, In: Proceedings of the First International Conference on Multi-Agent Systems (1995)276–282Google Scholar
  9. 9.
    Nash, J.R: Non-cooperative Games, Ann. of Math. 54(1951)286–295CrossRefMathSciNetGoogle Scholar
  10. 10.
    Nwana, H.S., Lee, L.C., Jennings, N.R.: Coordination in Software Agent systems, BT Technology Journal, Vol.14,No.4(1996)79–88Google Scholar
  11. 11.
    Orlovski, S.A.: On Programming with Fuzzy Constraint Sets, Kybernetics 6, (1977)197–201 (Reference from [6])CrossRefGoogle Scholar
  12. 12.
    Orlovski, S.A.: Fuzzy Goals and Sets of Choices in Two-person Games. In: Kacprzyk, J., Fedrizzi, M.(eds.): Multiperson Decision Making Models Using Fuzzy Sets and Possibility Theory. Kluwer Academic Publishers, Dordrecht(1990)288–297Google Scholar
  13. 13.
    Ragade, R.K.: Fuzzy Games in the Analysis of Options. J. Cybem. 6, (1976)213–221. (Reference from [6])MathSciNetCrossRefGoogle Scholar
  14. 14.
    Rasmusen, E.: Games and Information: An Introduction to Game Theory. Basil Blackwell, Oxford(1989)zbMATHGoogle Scholar
  15. 15.
    Rosenschein, J.S., Genesereth, M.R.: Deals among Rational Agents. In: Proceedings of the Ninth International Conference on Artificial Intelligence (1985)91–99Google Scholar
  16. 16.
    Sakawa, M., Nishizaki, I.: A Lexicographical Solution Concept in an n-Person Cooperative Fuzzy Game. Fuzzy Sets and Systems, Vol.61(3), (1994)265–275zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Sakawa, M., Kato, K.: Interactive Decision-making for Multi-objective Linear Fractional Programming Problems with Block Angular Structure Involving Fuzzy Numbers. Fuzzy Sets and Systems. Vol.97 (1998)19–31CrossRefMathSciNetGoogle Scholar
  18. 18.
    Tennenholtz, M.: On Stable Social Laws and Qualitative Equilibria. Artificial Intelligence Vol.102(1998)1–20zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Wu, S. H., Soo, V. W.: Escape from a Prisoners’ Dilemma by Communication with a Trusted Third Party. In: Proceedings of the Tenth International Conference on Tools with Artificial Intelligence. IEEE, Taipei(1998)58–65Google Scholar
  20. 20.
    Zimmermann, H.J.: Fuzzy Sets, Decision Making, and Expert Systems. Kluwer Academic, Boston(1986)Google Scholar
  21. 21.
    Zimmermann, H.J.: Fuzzy Set Theory and its Applications. 2ed. Kluwer Academic, Boston(1991)zbMATHGoogle Scholar
  22. 22.
    Zlotkin, G., Rosenschein, J. S., Compromise in Negotiation: Exploiting Worth Functions over States, Artificial Intelligence Vol. 84(1996) 151–176CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Shih-Hung Wu
    • 1
  • Von-Wun Soo
    • 1
  1. 1.Department of Computer ScienceNational Tsing Hua UniversityHsin-Chu CityTaiwan, R.O.C.

Personalised recommendations