Dynamic investment in online advertising of multi-oligopoly competitive enterprises with spillover effect

This paper aims to provide solutions to the dynamic investment strategies of online advertising for multi-oligopoly enterprises. Specifically, by considering the spillover effect of online advertising, the investment cost function incorporating the characteristics of online advertising is constructed and then combined with external interference factors, and the dynamic investment decision-making model of online advertising of three oligarchic competitive enterprises is constructed. Subsequently, using the Hamilton–Jacobi–Bellman function, the Nash equilibrium solutions of the online advertising amount and profits are attained in symmetrical, semisymmetric, and asymmetric cases. We then calculated and empirically analysed the share of the market. Finally, the model is extended to n-dimensional space. Our study suggests that (1) investment in fixed-location online advertising is inversely proportional to the spillover effect, while the amount of pay-per-click online advertising investment is directly proportional to the spillover effect. (2) In the semisymmetric case, enterprises with a low initial share are easily affected by the spillover effect, while in the semisymmetric and asymmetric cases, dominant enterprises are more easily affected by the spillover effect. (3) The amount of investment in online advertising is inversely proportional to external interference factors. (4) When there are more than three enterprises in the market, the profit is negative, indicating that new enterprise should be cautious about entering the industry.