<p>The Pareto solutions in multi-objective non-cooperative games represent a powerful tool for analyzing conflicts where players have multiple, non-aligned objectives. By providing a means of achieving balanced outcomes, Pareto solutions enable the identification of equilibria that are robust across various fields, from economic modeling to engineering design. In this paper advance our understanding of non-cooperative games, particularly under conditions of inconsistency where achieving a full equilibrium is not feasible. Considering the definition of the "Pareto minimum solution" of an inconsistent system, the existence of a solution of this multiobjective function for non-cooperative game are obtained. As multi-objective non-cooperative games continue to grow in complexity, the study of Pareto solutions will remain central to addressing the practical challenges of optimizing conflicting goals in competitive settings, thereby broadening the applicability of game theory to a range of modern, real-world problems.</p>