This paper concerns an aerial three-body multiobjective game (MOG) and deals with finding and sorting the control strategies by a novel solution concept. The MOG is a biobjective game, which involves a navigating aircraft that pursues a maneuverable target, in the presence of a threatening bleeding-energy missile. This biobjective game, which is hereby referred to as the main game, is defined as a payoff vector game, which means that the players are undecided about their objective preferences. Using a coalition between the missile and the target, an auxiliary two-sided nonzero-sum differential game is devised, which provides a closed-loop control law for each of the adversarial sides. Each of these control laws compromises between the two objectives of the main game, according to a selected safety-level parameter. By applying various values of the safety-level, each side is provided with a set of possible control strategies that it should select from. A novel rationalizability solution concept is applied on the sets of all possible control strategies of the players, which yields a set of rationalizable strategies (SRS) for each of the involved sides with respect to the main game. Furthermore, the obtained SRSs are analyzed, using a multicriteria-decision-analysis technique, in order to support the decision processes.