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This paper develops a mathematical tool for modelling market power cost in transmission expansion planning decisions. The mathematical modelling is based on the game theory in applied mathematics and the concept of social welfare in microeconomics. We assume the generating companies as Cournot players and the Transmission System Operators as a regulated social transmission planner. To tackle the multiple Nash equilibria problem, the concept of worst-Nash equilibrium is defined and mathematically formulated. The developed mathematical structure is a mixed-integer linear programming problem. This closed form mathematical structure can be solved efficiently using the available computational packages.