<p>This paper considers the investment coordination problem for the long term transmission capacity expansion in a situation where there are multiple regional Transmission Planners (TPs), each acting in order to maximize the utility in only its own region. In such a setting, any particular TP does not normally have any incentive to cooperate with the neighboring TP(s), although the optimal investment decision of each TP is contingent upon those of the neighboring TPs. A game-theoretic interaction among the TPs does not necessarily lead to this overall social optimum. We, therefore, introduce a social planner and call it the Transmission Planning Coordinator (TPC) whose goal is to attain the optimal possible social welfare for the bigger geographical region. In order to achieve this goal, this paper introduces a new incentive mechanism, based on distributed optimization theory. This incentive mechanism can be viewed as a set of rules of the transmission expansion investment coordination game, set by the social planner TPC, such that, even if the individual TPs act selfishly, it will still lead to the TPC's goal of attaining overall social optimum. Finally, the effectiveness of our approach is demonstrated through several simulation studies.</p>