Linear dynamic games with polytope strategy sets

摘要

This brief investigates the discrete time, linear dynamic games with finite horizon payoff functions. By resorting to the semi-tensor product of matrices, the authors prove that the linear dynamic game is a potential game. Then, they confine their attention to a special case: the strategy sets of game are polytopes. In this case, the searching Nash equilibrium problem for the linear dynamic game converts into one for a finite game. Furthermore, two different algorithms are designed for searching Nash equilibrium. Finally, an example is employed to validate the proposed algorithms.