轨道交通SBOT项目特许期的合作博弈模型研究

Cooperative Game Model on Concession Period in SBOT Project under Uncertainty

轨道交通SBOT模式是一种新的BOT衍生模式。特许期作为SBOT项目特许权协议的关键决策参数之一,对于轨道交通项目运作的成功与否至关重要。考虑到轨道交通SBOT项目的不确定性特征,在综合评估项目经济和社会效益的基础上,利用实物期权理论中经典的不可逆投资模型,构建了不确定条件下SBOT项目的特许期决策模型,其决策程序分为两步:首先,根据不可逆投资理论分别构建了项目各投资主体的最优投资时机决策模型,得到特许期的可行区间;为进一步讨论特许期的均衡解,根据合作博弈理论,利用公共部门/私营部门的扩展NPV函数,构建了以合作双方整体利益最大化为决策目标的特许期计算模型,求解出特许期的合作均衡解,并分析了均衡解的性质,最后通过算例对轨道交通SBOT项目特许期的合作博弈模型进行了验证。

As an effective solution to the problems of traffic congestion and emissions, urban rail transit has become China＇s key construction and investment fields. The shortage of capital is one of the biggest obstacles to restricting the development of urban rail transit. Subway line 4 in Beijing introduced a new form of BOT procurement model, namely SBOT （Subsidize in Building, Operate, and Transfer） model. Now, the SBOT procurement model has been widely adopted, such as subway line 4 in Beijing, subway line 14 in Beijing, subway line 1 in Hangzhou, etc. Concession period is one of the crucial decision variables in the arrangement of urban rail transit SBOT-type contracts. Projects with a shorter concession period could result in a higher toll/tariff regime transferred to the group of people who use the infrastructure facility. On the other hand, granting an excessively long concession period may result in government＇s loss. Since urban rail transit SBOT projects are characterized by irreversibility and uncertainty, project values tend to be underestimated by ignoring the value of the option to defer in the evaluation process. Therefore, concessionaire requires long concession periods. Therefore, the option to defer should be included when determining a reasonable concession period of SBOT projects under uncertainty. Existing literature for urban rail transport SBOT pattern is still in the exploratory stage, which has yet to see reports of right SBOT quantitative research on concession periods. However, the existing literature on the quantitative study of the concession period focuses on traditional BOT projects and is based mainly on the combination of net present value （NPV） method and game theory. The NPV method, however, cannot properly capture managerial flexibility value in SBOT projects. Besides, none of these decision-making models addresses additional social benefits or costs that BOT project may present. Urban rail transit is considered a green transportation with many tangible and social benefits, such as energy saving, safe, comfort, fast and efficient. Therefore, the quantitative study of the concession period should consider both economic and social benefits associated with urban rail transit projects. To overcome the limitations of the existing decision making models on concession-period, this research presents an alternative method to defining the concession period for SBOT projects using real options and cooperative game theory, as well as considering both economic and social benefits. The optimal concession period can be identified through two procedures： First, classical irreversible investment models, which view investment opportunities as perpetual American call options, are used to construct decision-making models of public sector/private sectors on investment in SBOT projects under dynamic uncertainty. A feasible interval for concession period is determined. Furthermore, the research sets concession periods as a decision variable, develops the real option model based on extended NPV function, and proposes a cooperative game model to maximize the sum of the two party＇ payoff functions. The paper derives the equi- librium solution in cooperative game. Finally, an example of urban rail transit SBOT project is applied to demonstrate the decision-making model of concession period under uncertainty. This research provides a new perspective and a reference for the public and private sectors to determine the equilibrium solution of concession periods for urban rail transit SBOT projects.