This paper analyzes competing firms' advertising strategies in markets characterized by dynamic market sizes with advertisement effect function. For new product innovations, a large literature has been developed on the basis of the celebrated Bass diffusion process, which captures what we call market-size dynamics. On the other hand, important theoretical and empirical insights have recently been obtained using the famous Lan chester warfare model of competition, with market-share dynamics. But, all of conclusions were infered by the constant advertisement effect. Our paper seeks to establish an advertisement effect function. In doing so, we will address the issue of optimal advertising strategies incorporating both market-share dynamics and market-size dynamics with a variable advertisement effect.
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