The Assignment Model is a basic optimization problem of Operations Research, which, by use of the Hungarian method, is always guaranteed to find an optimal solution but is of polynomial time complexity of O(n3). In this paper, we introduce another strategy which involves the use of game theory- namely, a min-min saddle point strategy- to effectively solve assignment problems. The suggested approach makes the computation simpler and more structured by hierarchically finding minimum row and column values, choosing the minimum global values as saddle-points, and repeatedly removing rows and columns in which they are set to considerable positions until an optimal allocation has been reached. The experimental test of 40 benchmark problems shows the approach to obtain solutions comparable to the Hungarian method with a high level of space and time efficiency. The study provides a new synthesis of game theory in assignment optimization, and its practical implementation in the field of management, engineering, and decision-making when the task is the allocation of resources. These results suggest the effectiveness of game-theoretic reasoning to classical optimization issues and that it can be used widely in modern resource allocation mechanisms.