We develop and apply several novel methods quantifying dynamic multi-agent team interactions. These interactions are detected information-theoretically and captured in two ways: via (i) directed networks (interaction diagrams) representing significant coupled dynamics between pairs of agents, and (ii) state-space plots (coherence diagrams) showing coherent structures in Shannon information dynamics. This model-free analysis relates, on the one hand, the information transfer to responsiveness of the agents and the team, and, on the other hand, the information storage within the team to the team's rigidity and lack of tactical flexibility. The resultant interaction and coherence diagrams reveal implicit interactions, across teams, that may be spatially long-range. The analysis was verified with a statistically significant number of experiments (using simulated football games, produced during RoboCup 2D Simulation League matches), identifying the zones of the most intense competition, the extent and types of interactions, and the correlation between the strength of specific interactions and the results of the matches.