Additional transmission capacity can improve the performance of the electricity market from two perspectives: firstly, efficiency benefit in terms of improving the social welfare of the electricity industry; and, secondly, competition benefit that leads to increasing competition among generating companies. This paper introduces an algorithm to model both the efficiency and competition benefits of additional transmission capacity in the process of transmission augmentation. The economic mathematical model is developed based on game theory in applied mathematics and the concept of social welfare in microeconomics. Transmission network service providers, generating companies and market management companies are placed in different stages of the developed model. The multiple Nash equilibria problem is tackled through the introduced concept of worst-Nash equilibrium. A numerical algorithm is designed to solve the developed model. The Garver's and IEEE 14-bus example systems are carefully modified to suit the purpose of this study; the former is used for conceptual evaluation of the algorithm, and the latter for testing the developed numerical solution. The results show that the proposed approach can improve the efficiency of the electricity market and reduce the market power in the generation sector using the transmission augmentation policies.