This paper discusses the transmission planning problem in a transmission network with multiple transmission planners. Each transmission planner is responsible for a region of the transmission network and maximizes its own region social welfare taking into account the transmission planning decisions of other transmission planners. The mathematical formulation of non-cooperative transmission planning problem is proposed. This problem is modeled using the multiple-leaders single-follower game in applied mathematics. The solution concept of the worst-Nash equilibrium is introduced to solve the set-up game. Different mathematical techniques are employed to formulate the worst-Nash equilibrium solution as a mixed-integer linear programming problem. A discussion on two possible applications of the derived mathematical structure is provided. The computational complexity is also discussed. The Three-Region IEEE-RTS96 example system is employed and modified to suit the purpose of analysis. The cooperative solution where the transmission planners merge into one single transmission planner is assumed as the benchmark in this study. The cooperative transmission planning is formulated in Appendix A of the paper. The results demonstrate the utility of the proposed solution in multi-regional transmission planning.