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Complementarity problems are recognized to be a general computational method for solving economic equilibrium models. There exist various problems describing the energy markets that rely on the complementarity models since they allow to analyze the interactions among different market players. Complementarity models generalize linear and non-linear problems because the Karush- Kuhn-Tucker optimality conditions are one particular instance of a complementarity problem. Moreover, the class of complementarity models is appropriate for modeling spatial price equilibrium, perfect and imperfect completion models, such as Cournot-Nash games, and other many models where both primal and dual variables can be constrained together. The first part of this paper provides a motivation and a description of complementarity models. In the second part, we investigate a capacity expansion problem applied to the restructured Italian electricity market that is currently subject to the European Union Emissions Trading System (EU-ETS). In accordance with the Kyoto Protocol, the EU-ETS aims to reduce greenhouse gas emissions from human activities provoking climate changes. This scheme is now subdivided into three phases and it is based on a cap and trade system that defines the maximum amount of CO2 that can be emitted in each compliance period. Our analysis shows that investments in renewables are mainly conditioned to incentive policies. The solution of the developed model is found by exploiting the mixed complementarity theoretical framework. The model is implemented in GAMS using the PATH solver. [ABSTRACT FROM AUTHOR]