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This paper explains the use of game theory to be applied for spectrum sharing scenario in unlicensed bands. A multi variable payoff function  is used to illustrate the process of achieving Nash-Equilibrium by varying the various modulation schemes and power for two non-cooperative systems sharing the same spectrum. This non-cooperative spectrum sharing often leads to a situation where one system is at a disadvantageous position. The situation can be improved if a global utility function is considered that represents a fairness objective. A modified global utility function is proposed that improves the Nash-Equilibrium condition for the two systems scenario than the already existing ones.