This paper proposes a Three-Stage Model for transmission augmentation in restructured electricity markets. The mathematical formulation of the model is developed based on the game theory. Transmission Network Service Provider, TNSP, Generating Companies, GenCos, and Market Management Company, MMC, are placed in different stages of the model. These stages are linked to each other using the Leader-followers game and the concept of Nash equilibriums. An increase in transmission capacity can have two benefits for the electricity market; firstly, efficiency benefit in terms of improving the social welfare of the electricity industry, and, secondly, competition benefit which leads to increasing competition among generating companies. The introduced Three-Stage Model can capture both benefits of transmission projects in electricity markets. An effective numerical method is designed for solving the developed Three-Stage Model. A modified IEEE 14 example system is employed to show the effectiveness of the methodology. This paper has been organized in two parts. First part deals with the mathematical formulation of the algorithm and second part deals with the numerical studies. What follows is the first part of the paper.