1 Abstract—This paper is the second of a two-paper series and presents a model to assess and promote investment projects defined in a plan of expansion of the transmission. We propose a model that consists of three main elements: valuation of a project based on the design of a linear contract, a principal-agent model to assess the optimal effort of an agent and the right-of-way negotiating cost. We also define a model to evaluate bids by the agents. The value of the project depends on the number of competitors, the incentives to invest, and the right-of-way costs. The right-of-way cost is approached from the perspective of a bilateral bargaining problem. We analyze two case studies. The first is a plan to expand the IEEE 24-RTS system. The second is based on the expansion plan of the Central Interconnected System (SIC) of Chile. The results show that the principal-agent model obtains the real costs of the bidders and creates incentives for disclosure of information. This creates optimal offers that depend on the incentive generated by the social planner. Index Terms—Transmission expansion planning, game theory, design mechanism, principal-agent, incentive and bidding contract. NOMENCLATURE A. Indexes j Index of projects. n Index of investors. o Index of land’s owners. M Index of mandatory allocation rules. RoW Index of bargaining solutions between agents n and o. Z Expansion plan done by a centralized planner. S Set of pairs of payments where the players act cooperatively. B. Decision Variables w j V Expected value of the winning bid for project j [M$]. w j b Expected winning bid for project j [M$]. This work was supported in part by CONICYT-Programa en Energías 2010, Pontificia Universidad Católica de Chile, Fondecyt, MECESUP(2), Transelec and the Ministry of Science and Innovation of Spain grant ENE2009-09541. J. D. Molina and H. Rudnick are with the Electrical Engineering Department, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile (email: jvmolinac@uc.cl; hrudnick@ing.puc.cl) J. Contreras is with E.T.S. de Ingenieros Industriales, University of Castilla − La Mancha, Campus Universitario s/n, 13071 Ciudad Real, Spain (email: Javier.Contreras@uclm.es) n j b Expected investor’s bid for project j [M$]. * n j c Expect optimal cost for an investor n in project j [M$]. RoW j x Expected right-of-way cost of the bargaining solutions of project j between agent n and o [M$]. n M j d , Payment pair when agents n and o act non- cooperatively (disagreement point). n j I Expected income determined by T j n – g j n . n j g Effort cost function of investor n determined by 0.5  j n  (e j n ) 2 . n j e Effort value to reduce the cost of project j [M$]. n j T Linear payment function T j n expressing the monetary transfer to the investors n determined by  j n +  j n   j n . n j  The degree of risk assumed by the investor n (if it does not assume any risk,  j n = 0 and if it assumes all the risks,  j n = 1). n j  Profit function determined by  j n e j n + w j n . j  Cost-share factor where the linear contract is of the incentive-type. C. Random Variables n j  Unpredictable cost of project j [M$]. n j w Random variable of profit function, w j n N[0, ( j n ) 2 ]. D. Constants n j c Reference value of project j [M$]. N Number of investors that participate in the tender of project j. n j  Effort coefficient reflecting the ability of the agent n to build a project j. n j  The positive coefficient of effort cost of investor n to project j.   2 n j  Variance of the project valuation j by investor n. n j  Degree of risk aversion of investor n for project j. o n j ,  Negotiation factor between agents n and o. n j z Minimum profit or income to reinvest in project j by investor n. n j  Fixed transfer in linear payment function T j n . A Principal-Agent Approach to Transmission Expansion  Part II: Case Studies Juan D. Molina, Graduate Student Member, IEEE, Javier Contreras, Senior Member, IEEE, and Hugh Rudnick, Fellow, IEEE