The development of social infrastructure is an important task of the state to improve the quality of life. If the public sector is not able to provide a sufficient number of social infrastructure, it is necessary to involve the business sector to pool resources. Public-private partnership is one of the tools to implement social infrastructure projects. The cooperation within the PPP enables the resources of the private sector to meet social needs that is the state’s responsibility. The article presents the different definitions of PPPs and highlights its main characteristics. To create the alliance «government – private sector» is not always possible. Thus, the article analyzes how to establish cross-sector partnerships, identifies factors affecting their formation, stability and development. It proposes to consider the formation of the PPP as a gradual process. The first stage is the analysis of the prerequisites for partnerships. The second stage is a preliminary selection of participants and the formation of a minimally acceptable set of companies for projects of social infrastructure. The article shows the characteristics and the basic principles of the selection. The third phase is to determine the winner of the competitive selection and, if necessary, to attract other companies that have passed the second stage. The final part of the article demonstrates modeling the situation using the apparatus of game theory, namely the description of the specific class of games that are appropriate in the PPP for their further study. The interaction between the state and construction companies to develop social infrastructure is considered as an example. In further research, the authors are planning to describe the strategies of the players in the classes of games and prove a theorem on the existence of such adjustment of the institutional environment in PPP projects, when there is a situation of strong Nash equilibrium for the considered classes of games. In other words, they intend to prove the feasibility of the projects of individual classes of games.