The transmission network switching is proposed in the literature as a way to improve social welfare in liberalized power markets. (7) Moreover, exercise of market power by strategic generating companies (Gencos) causes some extra cost in electricity market which can be alleviated by implementing appropriate switching policies. This paper contributes td the existing literature by developing a mathematical model that explores, from an economic perspective, the transmission network switching in the context of market power. The strategic Gecnos are modelled based on the Cournot game. The Nash equilibrium of the game between Gencos is formulated as an equilibrium problem with equilibrium constraint (EPEC). The EPEC problem is transformed to a mixed-integer linear feasibility problem. To handle the multiple Nash-equilibria situations, the solution concept of the extremal-Nash equilibrium (ENE) is introduced. A mixed-integer linear program (MILP) is derived for finding ENE. The transmission switching decisions are modelled as binary variables controlled by the system operator (TSO). The TSO minimizes the system dispatch cost calculated at ENE and network reconfiguration cost. The TSO minimizes the cost using its transmission switching decisions. The problem faced by the TSO is a mixed-integer bilevel linear program (MIBLP) with binary variables in both upper and lower levels. The upper level models the TSO's action and the lower level the oligopolistic Gencos (competing in Cournot game). A (parallel) branch and-bound technique is used to solve the developed MIBLP model. An illustrative 3-bus example system and the IEEE-RTS96 are modelled and carefully studied. (8)The numerical results demonstrate that: 1 - the (parallel) branch-and-bound technique can effectively solve the developed MIBLP, 2 - using the developed model, the system operator can change topology of the network by switching the lines in order to reduce the adverse effect of the strategic behaviour of Gecnos. (C) 2017 Elsevier B.V. All rights reserved.