Cooperation between supply chain partners in the oil industry is essential, especially when oil prices suffer from fluctuations that affect the profitability of each party. An essential task in oil field development projects is to create an optimum agreement between the national oil company and the international oil company to guarantee agreement optimization. In this paper, the national oil company is the first party (FP) and the international oil company is the second party (SP). The paper’s purpose is to investigate the use of game theory to obtain the best agreement between the FP and SP in order to enhance the cooperation and reduce conflict. In this paper, Nash and Maxi-min solutions have been applied for the first time in a special type of petroleum agreement, called exploration and production sharing agreements (EPSA). This is conducted for a case study in Libya. The study considers nine negotiation factors (issues) in the EPSA, which are the share percent, the four “A” factors, and the four “B” factors, which are usually affected by the fluctuations of oil prices; and the study investigates their effect on the total payoff function, the net present value (NPV), and internal rate of return (IRR) for both parties. The Maxi-min solution has shown an improvement in the NPV and IRR of the SP, where NPV increased from USD 148 million to USD 195 million, and IRR from 15.65% to 17.01%. The Nash solution has shown a little more improvement than the Maxi-min solution in the NPV and IRR for the SP, where the NPV and IRR have increased from USD 148 million to USD 222 million and from 15.65% to 17.94%, respectively.