Abstract
The purpose of the paper is to determine the behavior of Nash optimal open-loop advertising strategies of a dynamic duopoly. The logarithmic two-person nonzero-sum advertising differential game analyzed byJørgensen [1982] is extended to more general nonlinear functionsg (u 1,u 2) measuring the effectiveness of advertising expendituresu 1,u 2 of two firms with respect to the development of the market shares over time. It is shown that under the assumption of zero cross effects of the advertising efficiency function the main features of Jørgensen's model are preserved. Furthermore, two models with advertising rates interacting asymmetrically with respect to the marginal advertising effectiveness are studied. For zero salvage values of terminal market shares it is shown that the Nash optimal advertising expenditures of a small firm are always downward sloping, whereas the shape of a large competitor's advertising rate can only be determined under additional assumptions.
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