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Defining and making decisions about network investments has become a hard task in a competitive environment. This work defines a methodology to look for expansion alternatives in a transmission system. We propose a Transmission Expansion Game model that consists of four main elements: i) generating transmission expansion plan scenarios, ii) valuation of a project based on the design of a linear contract, bargaining solutions and hidden actions, iii) optimal value of a risky investor's portfolio made up of several projects, and iv) transmission cost allocation with wind energy assets. The results obtained show that the model developed is efficient to solve the combinatorial problem. A principal-agent model obtains the real costs of the bidders and creates incentives for disclosure of information. The private optimal portfolio and bargaining for allocation cost gives evidence for the central planner to adjust the project assignment process and to carry out the proposed expansion plan efficiently. To test the methodology we analyze the Chilean Central Interconnected System. [ABSTRACT FROM PUBLISHER]