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In the realm of game theory, strategic interactions pervade every facet of decision-making, from economics and political science to biology and computer science. These interactions, often characterized by uncertainty, have fueled the development of various game models to capture the subtleties of real-world scenarios. Among these models, interval games emerge as a powerful framework for addressing the inherent uncertainty and vagueness inherent in decision-making processes.

This paper deals with the intersection of noncooperative and cooperative interval games, offering novel insights into strategic interactions under uncertainty by introducing the interval α and β characteristic functions (CFs). We consider noncooperative two-player non-zero-sum interval games played between a coalition and players that are left out of the coalition and determine the interval α and β CFs for each coalition. Further, we compute the interval Shapley value and the interval core in the context of cooperative interval games and provide some numerical illustrations.