Abstract: The current new-type urbanization measures of Chinese government will pull tens of thousands of billions of investment in the infrastructure. However, the government's financial capital is so limited that it is difficult to meet the demand of a large number of infrastructure investment. Thus a model called PPP (Private-Public Partnership) is put forward to solve the shortage of government funding. The infrastructure project using the PPP generally has a quasi public goods attribute, which leads to its low operating revenue unable to take back the private huge initial investment. That means the proper compensation should be given to the private investor, if the government wants the PPP project to be successful. The compensation for the PPP project is not easy to determine before the event because the excessive or insufficient compensation will cause that the project's social welfare or the private interest is damaged. Only the compensation after the event will reduce the enthusiasm of private investment, which will also cause the compensation to be inefficient. Based on the governmental decision-making dilemma for the compensation, a single period compensation contract is introduced for the private investor. The contract specifies that the government should promise the concession revenue before the event to the private investor and then give a certain post-compensation to the investor by comparing the project's real revenue with the concession revenue.When the contract is accepted, the governmental compensation is likely to imply that the private investor show the excessive optimism and confidence on the PPP project's future expectation. That is,the private investor has the overconfidence behavior under the governmental compensation. For this reason, the private overconfidence is considered in the study on the governmental compensation contract for the PPP project.Firstly,the private investor's overconfidence is described by the "Mean-Variance" in which the private overconfidence coefficient is introduced. Thus the private expected utility function related to the overconfidence preference is proposed. Accordingly, the private overconfidence investment strategy is given out and its effect on the governmental optimal compensation contract is studied by the method of Stackelberg game. Secondly, under the circumstance that the private overconfidence can't be observed, the design and selection of governmental optimal compensation contract is discussed. Finally, the obtained conclusions are verified and expanded through a computing example.The studying results show that the private excessive investment behavior doesn't necessarily help to improve the expected social benefits for the project, but the government can always adjust the contract parameter to design the optimal compensation contract (maximizing the project's expected social benefit) which can adapt to the private different overconfidence behavior, and when the private excessive investment can't be observed, the government can select the optimal contract leading to the project's larger expected benefit according to the probability distribution for the private overconfidence.In summary, the results obtained in this paper not only contribute to the governmental compensation strategy, but also provide a better theoretical support for the implement of PPP project.

Key words: PPP project, compensation contract, overconfidence behavior, unobserved action