To control the “uniqueness” risk in Public-Private Partnership (PPP) projects of transportation infrastructure, we design a simplified “uniqueness” contract model by incorporating the impact of the initial investment which is based on the Bertrand model. The nonlinear programming method is adopted to derive the optimal “uniqueness” contracts for incumbent private capital, the public, and the social welfare, respectively. The simulation results show that the achievement of the optimal “uniqueness” contract is essentially the result of a compromise between the private capital, the public, and social welfare. The extent to which such a contract reduces the probability of “uniqueness” risk mainly depends on the equilibrium relation between the interests of private capital and the public. The initial investment is not related to the government default when the contract does not take into account the interests of the private capital. Furthermore, the “uniqueness” contracts between private capital and the government are mainly for anticompetitive purpose in the PPP market of transportation infrastructure. Unless the contract terms focus on the improvement of social welfare, entering a “uniqueness” contract will cause social welfare losses.

中文翻译：

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运输基础设施公私合营项目中的可持续性和最佳“唯一性”合同

为了控制运输基础设施的公私合营（PPP）项目中的“独特性”风险，我们通过结合基于Bertrand模型的初始投资的影响来设计简化的“独特性”合同模型。采用非线性规划方法分别得出现有私人资本，公共和社会福利的最优“唯一性”契约。仿真结果表明，最佳“唯一性”契约的实现本质上是私人资本，公共和社会福利之间折衷的结果。这种合同在多大程度上降低了“独特性”风险的可能性，主要取决于私人资本与公众利益之间的均衡关系。当合同未考虑私人资本的利益时，初始投资与政府违约无关。此外，在运输基础设施的PPP市场中，私人资本与政府之间的“唯一性”合同主要是为了反竞争目的。除非合同条款侧重于改善社会福利，否则签订“唯一性”合同将造成社会福利损失。