Bilinear differential game for competitive advertising with stochastic disturbance and abrupt impact

The estimated spending on online advertising worldwide will reach $520 billion during 2023, almost double compared with that in 2019. Due to the conjunction of huge expenditure and latent inefficiencies, competitive advertising has always been occupying a front-and-center place in marketing, among which research modeled as bilinear differential game is one of the most important. However, by the intrinsic difficulties of mathematics, there is no extant research to augment the analysis with Markov jump process, which is of particular significance to abrupt product-harm crisis or promotion interactions. Motivated by this requirement, iterative algorithm with convergence proof is developed to approximate bilinearity. Kalman filter and nonlinear separation theorem, which enable noise-contaminated sales data for analysis in the partial observation, are also introduce to hone in more actionable and focused in real business. The Simulink modeling in this paper provides a straightforward tool for rapid prototyping of these complex, time-varying, multilayer systems. The simulation model proposed allows automatically exploring competitions and finding the most efficient strategies. Moreover, six application examples, resulting from the permutations of four encounters with different time durations and abrupt impacts, have discovered eight implications. They not only complement the existing work on crisis, but also generalize to promotion, which imply that managers should anticipate the sales bump and optimally increase ad spending ex ante. Most importantly, they have revealed a number of new legal, advertising, competition and partly counterintuitive insights for those struggling to develop successful advertising strategies.

Automated summary

The estimated spending on online advertising will almost double and reach $520 billion in 2023 compared to 2019. Competitive advertising, especially research modeled as a bilinear differential game, plays a significant role in marketing due to the large expenditure and inefficiencies. However, there is currently no existing research that incorporates Markov jump process into the analysis, which is crucial for abrupt product-harm crisis or promotion interactions.