J. Binner, L. Fletcher (Aston Business School) and V. Kolokoltsov (Statistics, Warwick University) suggest and analyze a dynamic model describing the changes to market shares in a duopoly caused by strategic investments in advertising, where firms aim at maximizing the discounted flow of profits Unlike usual models, where the firms are correcting their rate of investment continuously (which leads to difficult to analyse positional differential games) we assume from the beginning that the rate of strategic investment is constant for each firm. This allows for a much simpler and partially explicit analysis. From the practical point of view this approach is meant to be used recursively by fixing the rate for a certain (large or small) time and re-evaluating the strategy each planning period.

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