Advertisement

Constrained Matrix Games with Fuzzy Payoffs

  • Tina VermaEmail author
  • Amit Kumar
Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 383)

Abstract

In this chapter, flaws of the existing methods [4, 5, 6, 7] for solving constrained matrix games with fuzzy payoffs (constrained matrix games in which payoffs are represented by fuzzy numbers) are pointed out. To resolve these flaws, a new method (named as Vaishnavi method) is also proposed to obtain the optimal strategies as well as minimum expected gain of Player I and maximum expected loss of Player II for constrained matrix games with fuzzy payoffs. To illustrate the proposed Vaishnavi method, some existing numerical problems of constrained matrix games with fuzzy payoffs are solved.

References

  1. 1.
    Charnes, A.: Constrained games and linear programming. Proc. Natl. Acad. Sci. USA 39, 639 (1953)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Dresher, M.: Games of Strategy Theory and Applications. Prentice-Hall, New York (1961)zbMATHGoogle Scholar
  3. 3.
    Kawaguchi, T., Maruyama, Y.: A note on minimax (maximin) programming. Manag. Sci. 670–676 (1976)Google Scholar
  4. 4.
    Li, D.F.: Fuzzy constrained matrix games with fuzzy payoffs. J. Fuzzy Math. 7, 907–912 (1999)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Li, D.F., Cheng, C.T.: Fuzzy multiobjective programming methods for fuzzy constrained matrix games with fuzzy numbers. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 10, 385–400 (2002)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Li, D.F., Hong, F.X.: Solving constrained matrix games with payoffs of triangular fuzzy numbers. Comput. Math. Appl. 64, 432–446 (2012)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Li, D.F., Hong, F.X.: Alfa-cut based linear programming methodology for constrained matrix games with payoffs of trapezoidal fuzzy numbers. Fuzzy Optim. Decis. Mak. 12, 191–213 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Owen, G.: Game Theory, 2nd edn. Academic Press, New York (1982)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoparRupnagarIndia
  2. 2.School of MathematicsThapar Institute of Engineering and TechnologyPatialaIndia

Personalised recommendations