Strategic behaviors in electricity markets are analyzed. Three related topics are investigated. The first topic is a research about the NE search algorithm for complex non-cooperative games in electricity markets with transmission constraints. Hybrid co-evolutionary programming is suggested and simulated for complex examples. The second topic is an analysis about the competing pricing mechanisms of uniform and pay-as-bid pricing in an electricity market. We prove that for a two-player static game the Nash Equilibrium under pay-as-bid pricing will yield less total revenue in expectation than under uniform pricing when demand is inelastic. The third topic is to address a market power mitigation issue of the current Texas electricity market by limiting Transmission Congestion Right (TCR) ownership. The strategic coordination of inter zonal scheduling and balancing market manipulation is analyzed. A market power measurement algorithm useful to determine the proper level of TCR ownership limitation is suggested. / text