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This paper addresses the problem of optimally coordinating connected vehicles crossing an intersection without any explicit traffic signals. We propose a game-in-game framework that utilizes Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) technologies in order to maximize intersection throughput and to minimize traffic accidents and congestion. A Platoon Structure Formation Algorithm (PSFA) is proposed to form coalitions for CAVs at the intersection boundary, and a strategic game for CAVs in the interior is proposed to avoid predicted accidents inside the intersection. We perform extensive experiments to evaluate our proposed game-in-game framework under different traffic conditions. The results show that our proposed game-in-game framework reduces the accidents by 99%, while increasing the intersection throughput significantly.