Refinements of Nash equilibrium in a Pentagonal Fuzzy Bimatrix Game

In this paper, we introduce the concept of symmetric pentagonal fuzzy bimatrix and constant pentagonal fuzzy matrix for which we define the existence of Nash equilibrium in both pure and mixed strategies along with some numerical illustrations. By applying Ranking to the pay-offs, we convert the fuzzy valued game problem to crisp valued game problem. Therefore, Solution concept of perfect equilibrium for normal form game is reviewed and a new concept of proper equilibrium of pentagonal fuzzy bimatrix game is discussed.