In risk allocation process, it is not correct to pass the whole responsibility of some risks to the contractor. The reason is that some defensive strategies such as lowering the work quality and lodging claim and litigation may be implemented by the contractor that may increase the project cost and duration. It is therefore necessary to share the responsibility of these risks between contracting partiesandin the other words to perform the risk allocation process quantitatively. In the negotiation process performing to determine the percentage of risk allocated to each of the contracting parties, there exists a willing to cooperate and reach an agreement in spite of the existed conflicts in the revenues of these parties. In this research, the game theory that is the study of mathematical models of conflict and cooperation between intelligent rational decision-makers is used for quantitative risk allocation. The proposed model presents a powerful tool that satisfies desirable criteria such as efficiency and fairness and the equitable percentage of risk allocation is determined. To evaluate the capabilities and performance of the proposed model, it is implemented in sample project and the risk allocation percentage between the client and contractor is determined for one of the identified risks.