On the solution of a differential game of managing the investments in an advertising campaign (Q2284201)

The authors present a model of goodwill accumulation by several companies during their advertising campaigns. The problem is viewed as an \(n\)-person nonzero-sum differential game. In Section 1, they give the problem statement and describe the dynamics of the game and the payoff function. In Section 2, they obtain a solution for the cooperative statement of the game, specifically, they give a detailed analysis of the selection of a solution among four possible candidate functions. In Section 3, they prove that, in the noncooperative variant of this game, the system of algebraic equations for finding the coefficients of the Bellman function also has two solutions; and an analysis is carried out to choose the appropriate solution. Conclusions are formulated in Section 4.