Delayed and cumulative effects of advertising in a cooperative or competitive environment

In this talk, I investigate the goodwill dynamics evolved à la Nerlove–Arrow in which delayed or cumulative effects of advertising is included. As a result, a cooperative differential game is formulated for which I investigate the optimal solution and analyse some properties of it. In the second part of the talk, I discuss some open questions related to a non-cooperative differential game with delayed or cumulative effects in controls.