In this paper, we generally study performance of some network routing algorithms. These are Kruskal's, Prim's and Sollin's algorithms as tree algorithms that are used in minimum spanning trees problems. Further, we propose new algorithms that are modeled by game-theoretical approach. Mathematical models have been used to solve complex problems such as those in social sciences, economics, psychology, politics and telecommunication. In this context, game theory can be defined as a mathematical framework consisting of models and techniques analyzing the behavior of individuals concerned about their own benefits. Game theory deals with multi-person decision making, in which each decision maker tries to maximize own utility or minimize own cost and is applied to networking, in most cases to solve routing and resource allocation problems in a competitive environment. Modeling the network scenarios with the game-theoretical approach is one of the pioneering aims of the study. The algorithms for performance analysis are carried out OMNeT++, which is a network simulation program. Finally, the results are compared with each other and the literature.