This paper proposes a new methodology for synthesizing animations of multiple characters, allowing them to intelligently compete with one another in dense environments, while still satisfying requirements set by an animator. To achieve these two conflicting objectives simultaneously, our method separately evaluates the competition and collaboration of the interactions, integrating the scores to select an action that maximizes both criteria. We extend the idea of min-max search, normally used for strategic games such as chess. Using our method, animators can efficiently produce scenes of dense character interactions such as those in collective sports or martial arts. The method is especially effective for producing animations along story lines, where the characters must follow multiple objectives, while still accommodating geometric and kinematic constraints from the environment.