Highway system is vital in urban transportation network. Operating, maintaining and financing of existing highway (a.k.a. brownfield highway) are increasingly important. Public-Private Partnership(PPP) is implemented in various countries to solve problems in urban transportation infrastructure projects. In this paper, we will mathematically model PPP to discuss whether government could achieve social optimum for free in urban highway PPP project. Previous modelling methods in PPP share two common shortcomings: over-simplified assumption on behavior of users and owners of the highway and insufficient attention to privately-held information. In this paper, we create a new form of PPP, improved Investment Public-Private Partnership using mechanism design as a multi-leader-multi-follower (MLMF) Stackelberg game. The implementibility in MLMF Stackelberg game in dominant strategy and Bayesian equilibria are derived and the feasibility of the model is proved through these theorems. The condition is discussed and given on achieving social optimal and budget balance simultaneously, that is the government gets job done for free. The SiouxFalls network model is used to illustrate and verify the model.