We study a novel approach based on game theory for the identification of overlapping associations and hierarchical structures within a social network. The approach models association detection as a coalition formation game, where individuals in the network act as rational players striving to enhance the overall utility of their groups. To achieve this objective, players collaborate and establish alliances. Each player has the flexibility to join multiple coalitions, and smaller coalitions can merge with one another to create larger ones, as long as the merger leads to an improvement in the coalition’s utility. This approach enables the simultaneous identification of overlapping associations and hierarchical structures in the social network. The utility (service) function of apiece coalition is definite as a grouping of a income function and a price function. The income function events the extent to which the group’s objectives are enhanced, while the cost function counts the level of communication between coalition members and the remaining network. This article investigates two categories of methods based on cooperative and non-cooperative game, and reports the results of tests performed on both artificial and real-life network data. The findings demonstrate that the CoCo-game method and the overlapping method outperform other approaches and result in larger coalitions compared to the clique method and the CoCo-game method. Additionally, the CoCo-game method and the observation method indicate superior performance in identifying associations within clique networks, karate graphs, and Zachary graphs. Notably, in clique graphs, they exhibit exceptional performance of up to 90 percent. In the Zachary graph, they perform well by employing a value of μ = 0.1 for the cross edges section. Furthermore, in networks comprising 10000 nodes and 1000 edges, the CoCo-game method surpasses the clique method in terms of performance and exhibits reduced vertex overlap.