Journal of Systems Engineering and Electronics ›› 2010, Vol. 21 ›› Issue (1): 47-56.doi: 10.3969/j.issn.1004-4132.2010.01.009

• SYSTEMS ENGINEERING • Previous Articles     Next Articles

Fuzzy Nash equilibrium of fuzzy n-person non-cooperative game

Xiaohui Yu∗ and Qiang Zhang   

  1. School of Management and Economics, Beijing Institute of Technology, Beijing 100081, P. R. China
  • Online:2010-02-26 Published:2010-01-03
  • Supported by:

    This work was supported by the National Natural Science Foundation of China (70771010).


The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy number by its center of gravity or by the real number with its maximal membership. By reducing fuzzy number into a real number, we lose much fuzzy information that should be kept during the operations between fuzzy numbers. The fuzzy quantities or alternatives are ordered directly by Yuan’s binary fuzzy ordering relation. In doing so, the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games is shown based on the utility function and the crisp Nash theorem. Finally, an illustrative example in traffic flow patterns of equilibrium is given in order to show the detailed calculation process of fuzzy Nash equilibrium.