الفهرس 
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Abstract
In this thesis ,our focus lies on exploring the issue of uncertainty in player information with in the context of differential games ,utilizing the concept of ”rough sets” as an effective tool to tackle such problems . Specifically , we aim to investigate the Nash and Stackelberg equilibriums of a differential game where all players are exerting control which is considered to be rough and so is the state trajectory. We aim to investigate how roughness influences the equilibrium outcomes in the differential game . Two problems statement that are related to the rough nature of the differential games are formulated and tackled. The first problem centers around an investigation of the Nash equilibrium . The second problem explores the Stackelberg equilibrium, characterized by its hierarchical decision-making approach . In the context of the Stackelberg equilibrium , we consider two distinct scenarios : one involving dependent decision making by the followers and another involving independent decision-making by the followers . For the problems we address in this study our objective is to establish the necessary and sufficient conditions for attaining the Nash and Stackelberg equilibriums . Additionally ,we aim to determine the rough intervals associated with both the Nash and Stackelberg equilibriums and the state trajectory in the rough differential game . To address the challenge of roughness , we employ the trust measure method and the expected value method to transform the rough problem into acrisp one .By utilizing these transformation techniques , we aim to derive the α -trust Nash and Stackelberg equilibriums and the expected value Nash and Stackelberg equilibriums , which are dependent on the parameters α and μ , both of which reside within the interval [0,1].