Journal of Harmonized Research in Engineering

GAME WITH FUZZY PAYOFFS AND CRISP GAME

Abstract

Author(s): Arti Chouksey and Sonal Bharti

In this paper we consider a bi-matrix game with fuzzy payoffs. To compare a fuzzy numbers, some different ordering operators can be used. We define Nash equilibrium in fuzzy game using the ordering op erator. The game with crisp payoffs is associated with the original game. Here, crisp payoffs are the operator’s value on a fuzzy payoff. We propose the following statement: if the ordering operator is linear, then the game with payoffs has same Nash equilibrium strategy profile as the crisp game. We present an algorithm for constructing a Nash equilibrium in a bi-matrix game with fuzzy payoffs and we are using this fact. We use such ordering operators, and construct the Nash equilibrium in examples of bi-matrix games. Key Word: Fuzzy set, bi-matrix, membership function, cooperative game