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.     

A Controllability Study for a Team Linear Quadratic Game

A controllability interpretation of team linear quadratic games, with one performance index for the team in competition with one common opponent, is conducted to provide criteria of choice of terminal unknowns for the optimal game solution and to facilitate the computations of the trajectories. Efficiency of the pursuers is expressed in terms of the team controllability. The criteria provide a perfect choice for particular team dispositions named "optimal teams," which are shown to neutralize the evader. The study produces a particularly simple method to dispose or place a team optimally and to compute the corresponding optimal solution.