The impact and efficacy of a cap-and-trade regulation on the electric power industry depend on interactions of demand elasticity, transmission network, market structure, and strategic behavior of generation firms. This paper develops an equilibrium model of an oligopoly electricity market in conjunction with a Cap-and-Trade emissions permits market to study such interactions. The concept of conjectural variations is proposed to account for imperfect competition in the permits market. We demonstrate the model using a WECC 225-bus system with a detailed representation of the California market. In particular, we examine the extent to which permit trading strategies affect the market outcome. We find that a firm with more efficient technologies can employ strategic withholding of permits, which allows for its increase in output share in the electricity market at the expense of other less efficient firms.