The first chapter is about market efficiency. Broadly, the primary objective of antitrust policy is to promote efficiency. However, economists do not measure efficiency directly. Rather, they use a less precise concept, market power, because it is thought that market power is more easily measured and correlated with efficiency. The Herfindahl and Lerner indexes are standard measures of market power. This paper explores the circumstances in which these two indexes are and are not reliable indicators of efficiency. In most models, both indexes are often not good proxies of efficiency. In addition, I show how to compute efficiency directly by using firm level output and market price. I conclude that it is not easier to measure market power than efficiency. The second chapter focuses on the dynamic properties of an oligopolistic market structure with stochastic successful probability of creating or maintaining investments for a firm. In each period of a game, a representative firm decides whether to have positioning (creating or maintaining) investments. All established firms compete either in the Bertrand or Cournot framework. By adopting symmetric Market perfect Nash equilibrium, firms choose strategies to maximize the discounted present value of cash flow. We obtain the steady state of the system and the expected duration for each state of the system in different market competitions. We also discover the efficiency level is higher in the Cournot rather than the Bertrand competition with different numbers of active firms in the market. The third chapter develops a theoretical model for the electricity sector in the presence of imperfect competition in a Cournot framework. By allowing market size, industry concentration, and technology to differ, the model incorporates transmission costs and transmission capacity. We identify the condition under which trade benefits a single country or increases global welfare by changing these asymmetric factors for each country. We discover that the expansion of transmission capacity between two countries is not always beneficial for a single country or for global welfare.