In this paper, Game Theory (GT) and its applications in power markets are introduced including the fundamental concept of Nash Equilibrium (NE) which is a universal and essential solution concept in GT. The system studied herein is a small system with 3 generation companies to find the best bidding strategies for each company and the market price to profit the whole market. In search for the NE, a numerical method based on the basic essential concept of GT, which is how the generation companies will interact with each other in a competitive commercial environment, has been successfully implemented and demonstrated on the 3-company system. The demand side is also introduced into the market as this also has a significant bearing on the bidding strategies and the market price. A comparison of numerical methodology to Genetic Algorithms (GAs) is made by implementing these into the same 3-company system. The results show that such a numerical method would be very inefficient for a commercial environment where hundreds of generation companies co-exist compared to GAs.