PARAMETER ANALYSIS OF A ZERO-SUM DIFFERENTIAL GAME APPROXIMATING A NONZERO-SUM GAME

In this paper we consider a zero-sum differential game in feedback setting with one state coordinate and finite time horizon. The problem is characterized by two parameters. This game arises as an approximation to a nonzero-sum game. Using analytical and numerical methods we solve the HJBI equation and give the description of the optimal feedback controls for both players. These feedbacks are given in terms of switching curves and singular universal lines. We also determine the change (bifurcations) of the optimal phase portrait of the game depending upon the parameters. In conclusion, we show that for some values of the parameters the solution of the considered zero-sum game leads to the exact solution of the corresponding nonzero-sum game, and for the other values of the parameters it supplies just some approximation.