Stackelberg game theory-based optimization model for design of payment mechanism in performance-based PPPs

Payment mechanisms lie at the heart of public-private partnership (PPP) contracts. A good design of the payment mechanism should consider the owner's goals in the project, allocate risks appropriately to stakeholders, and assure satisfactory performance by providing reasonable compensation to the private developer. This paper proposes a Stackelberg game theory-based model to assist public agencies in designing payment mechanisms for PPP transportation projects. The interests of both public and private sectors are considered and reflected by a bilevel objective function. The model aims to search for solutions that maximize a project's overall performance for the sake of social welfare while simultaneously maximizing return for the sake of private investment. A variable elimination method and genetic algorithm are used to solve the optimization model. A case study based on a real PPP project is discussed to validate the effectiveness of the proposed model. The solutions provided by the model reveal that the optimal payment mechanism structure could be established such that it would satisfy owners' requirements for overall project performance while optimizing project total payments to contractors.