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The history of oil contracts in the last century indicates that oil contracts are a form of conflict between the interests of foreign oil companies and national interests of reservoir-owning governments. In this context, an important question arises for reservoir-owning governments as to which existing conventional upstream contracts should be chosen to maximize benefits. Representation theory has been used to answer this research question. In the designed model, each party's interest function in each of the upstream contracts is identified and modeled. Also, the rationality and motivation conditions in this model have been analyzed as participation constraints. The results of the proposed model using the genetic algorithm method show that, given field coordinates, the production-sharing contract has the lowest representation cost compared to the other two contracts of concession and service purchase. And as the selected model, production-sharing contracts can make the most profit for reservoir-owning governments.

Game theory has a significant role in contemporary orthodox economics. This theory studies the strategic behavior of players. So strategic interaction is the key point in the games theory. Principalagent model is an application of the theory. This model is applied when a job or an activity is delivered to an agent by a firm or another agent called the principal. Naturally the terms and conditions including the rights and obligations of two sides are elaborated in the contract. Depending on whether the information on exact details of the subject and the terms are the same or not, different models are developed. One of the most important financing instruments in noninterest banking as a main field of Islamic Economics is profit-loss sharing contracts among which we can name sleeping partnership. The subject matter of sleeping partnership is trade in which a capital owner finances the money needed by the agent to start a business which is based on profit-loss sharing. This paper tries to construct an analytical model to explain the sleeping partnership by appling principal– agent model with asymmetric information case which is causing adverse selection .In this paper we showed that Islamic finance instruments (sleeping partnership) in the spirit of profit-loss sharing can be explained through the modern achievements of contemporary economics and we can analyze sleeping partnership with the help of game theory method.