In this thesis current questions regarding the functionality of liberalized electricity markets are studied addressing different topics of interest in two main directions: market power and competition policy on electricity wholesale markets, and network investments and incentive regulation. The former is studied based on the case of the German electricity market with respect to ex-post market power analysis and ex-ante remedy development. First an optimization model is designed to obtain the competitive benchmark which can be compared to the observed market outcomes between 2004 and 2006. In a second step the horizontal breaking up of dominant firms (divestiture) is simulated applying equilibrium techniques (the classical Cournot approach and the Supply Function Equilibrium approach). The later issue of transmission capacity investment is addressed by highlighting the complexity of network investments in electricity markets and by analyzing a regulatory mechanism with a two part tariff approach. The technical characteristics of power flows are combined with economic criteria and tested for different network settings.