Research On Differential Game Model Of Advertising Competition In Oligopolistic Market

The advertising investment strategy is one of the important strategies for enterprise in oligopolistic markets, which affect the enterprise's profits through to affect the market share, and make further influence on its survival and development. Therefore, the question of optimal advertising investment is always an analysis of the hot issues for business word and theory horizon. Since 1950's, people has shown great interest in the study for dynamic advertising investment, and obtained a wealth of research results. In this paper, the theory of differential game is used to study the three important interrelated issues in this area: First, the R&D investment is considered in the two-player advertising differential games; second, an N-player advertising differential game model is considered; third, the R&D investment is considered in the N-player advertising differential games. The research work and the results are as follows:First, the R&D investment is considered in the two-player advertising differential games. Assume that the two enterprises cooperate in R&D, but compete in advertising in the duopoly market. Enterprises make decisions on R&D and advertising so as to maximize the total expected profits. The theory of differential game is used to study the optimal strategies for enterprises'R&D and advertising, and the explicit Nash Equilibrium solution is obtained theoretically. Then the properties of the equilibrium solution are analyzed by the cases of symmetry and asymmetry. The research shows that, under certain conditions, enterprises'R&D increases profits; Optimal R&D strategy is affected by rival's advertising cost coefficient and other factors; the impact of the advertising cost coefficient on profits is greater than advertising influence coefficient; free-riding results in insufficient investment in R&D.Second, an N-player advertising differential game model is considered. The explicit closed-loop Nash equilibrium solution is usually difficult to obtain in the N-player differential game model, in many cases, they need to resort to numerical analysis. In this paper, an N-player advertising differential game model is constructed, and the explicit closed-loop Nash equilibrium is obtained by solving HJB equation. Then the effects of some relevant factors are analyzed for the optimal strategies and value functions. Results show that, besides of the common parameters such as the marginal revenue of advertising and cost function, other elements, e.g., the preference to future potential development, the time horizon, and the substitution of goods all have great influence on the optimal advertising.Third, the article constructed the N-player advertising model when considering the R&D investment. Because of the complexity of the problem and the time and energy limited, the basic ideas of Nash equilibrium solution are introduced mainly in this article; the important issues such as the existence of the explicit closed-loop Nash equilibrium remain to be further studied in future.The explicit closed-loop Nash equilibrium solution reflected the rational behavior in the dynamic game, so the research on it also has important practical significance. However, the theoretical analysis of explicit closed-loop Nash equilibrium solution is very complex and hard, so far, there are only a few differential game problems with explicit closed-loop Nash equilibrium solution. Therefore, this study not only have some significance for oligopoly advertising decisions , but also some theoretical value for the feature extraction of explicit closed-loop Nash equilibrium solution of the differential game.