On Team Games: A Computational Structural Analysis

Team games are studied here with one performance index for the team as a unit in competition with one common opponent. A structural analysis is presented with the intent to simplify the computation of optimal decision and communication processes. The minimum principle and calculus of variations are used to compute time-optimal and quadratic-optimal trajectories for certain linear "pursuit-evasion" games. A composition method is presented to compute an approximate solution to the two-versus-one problem from the solution to two one-versus-one problems. Help zones of a second pursuer to assist in the "capture" of an evader are derived. The hierarchical command and communication structure for a quadratic linear game of N pursuers and one evader is derived. An approximation is generated which has a convenient ripple or recursive structure.