This article analyzes advertising in an n-firm infinite horizon, differentiated products oligopoly. The firms all choose output and advertising levels in each period, and are assumed to behave noncooperatively. Advertising is characterized in a manner similar to capital: the effects of money spent on advertising today last well into the future. The interfirm advertising effect can be either cooperative or predatory, and in a linear-quadratic version of the model, this degree of cooperativeness is represented by a parameter. Existence and uniqueness of the Nash equilibrium are obtained, along with many comparative statics results.
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James W. Friedman (1983) studied this question.