This paper proposes an algorithm for autonomous strategic mission planning of missions where multiple unhabitated underwater vehicles (UUVs) cooperate in order to solve one or more mission tasks. Missions of this type include multi-agent reconnaissance missions and multi-agent mine sweeping missions. The mission planning problem is posed as a receding horizon mixed-integer constrained quadratic optimal control problem. This problem is subsequently partitioned into smaller subproblems and solved in a parallel and decentralized manner using a distributed Nash-based game approach. The paper presents the development of the proposed algorithm and discusses its properties. An application example is used to further demonstrate the main characteristics of the proposed method.