Feedback advertising strategies in a two-firm differential game: a numerical investigation

We present a procedure for finding feedback strategies numerically in a two-firm differential game (DG). To motivate the discussion, we start with the single-firm optimal control formulation of the problem with a linear revenue term and a nonlinear (quadratic) advertising rate cost term. We find the optimal control to maximise the firm's market share. When two firms compete for the market share, the optimal control model generalises to a …