Background: Multi-Criteria Group Decision Making (MCGDM) problems can be defined as the process of choosing the most suitable alternative among a set of alternatives. MCGDM problems can contain more than one participant, so the competition can possibly arise between the participants of any MCGDM Problem. MCGDM problems also contain complex, uncertain, incomplete, and imprecise information, so the crisp sets cannot be precious for representing this information. Objective: A new approach for solving the MCGDM problems which have competition between their participants under the condition of the uncertainty in data is proposed in this paper. In this approach, Single Valued Neutrosophic Sets (SVNs) is firstly used for representing the data uncertainty. Then, TOPSIS technique is extended to handle the SVN environment. After that, the game theory is used to find the optimal solution due to its superiority in dealing with the competition situations. Results: Finding the Nash equilibrium for the competitive MCGDM problem under neutrosophic environment (two-player non-constant sum game). Conclusion: The proposed technique opens the door of utilizing neutrosophic sets in conjunction with game theory principles in solving competitive MCGDM problems under uncertainty conditions.