Animating multiple characters to compete with each other is an important problem in computer games and animation films. However, it remains difficult to simulate strategic competition among characters because of its inherent complex decision process that should be able to cope with often unpredictable behavior of opponents. We adopt a reinforcement learning method in Markov games to action models built from captured motion data. This enables two characters to perform globally optimal counter-strategies with respect to each other. We also extend this method to simulate competition between two teams, each of which can consist of an arbitrary number of characters. We demonstrate the usefulness of our approach through various competitive scenarios, including playing-tag, keeping-distance, and shooting.