Oil and gas models are focused mainly in production, behavior, risk and forecast, so the present one constitutes a first attempt in trying to modellize oil sector behavior from the point of view of bargaining process. The purpose of this model, even if theoretically, is to present a theoretical approach of the bargaining process in oil and gas industry. I begin with a simple Nash bargaining solution including Edgeworth box for a better explanation of the behavior between two individuals that agree to participate in a bargaining process. Rubinstein’s model where two players, government and oil companies, have a common interest to bargain over the partition of a “cake”, but at the same time they have conflicting interests over the share of the cake and about the payoffs both of them could obtain from the bargaining situation. Even if this process can lead to an agreement, I take into account the risk of breakdown where one player or both may perceive that the negotiations might breakdown in a random manner for any reason that is not important for the outcome. The contract curve estimation shed light for analyzing the possibility to bargain about the selling and buying a commodity, in this first attempt, without taking into account the role of arbitrators and mediators, and any enforcement behavior from the part of each player.