Nowadays, public-private partnership projects have become a standard for delivering public services in both developed and developing countries. In this paper, we are concerned with the analysis of private sector proposals and the selection of the private sector partner to whom to award the contract. To the best of our knowledge, this problem has not been addressed within a game theory framework. To fill this gap, we model this decision problem as a static non-cooperative game of complete information and propose a new ordinal game theory algorithm for finding an optimal generalized Nash equilibrium. The proposed algorithm determines a single ranking of proposals or bidders that takes account of multiple performance criteria and reflects both the public sector and the private sector perspectives, and can handle any number of private sector players and any number of contractual terms. An illustrative scenario is provided to guide the reader through the workings of the proposed ordinal game theory algorithm. The proposed ordinal game theory-based analysis framework can be used by the private sector to analyse any set of potential proposals most likely to be submitted by bidders and to assist with the choice of bidding strategies, and by the public sector player to analyse any set of potential proposals most likely to be submitted under any set of contractual terms and to assist with the choice of a realistic set of contractual terms and their performance measures.