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The Bass diffusion equation is a well-known and established modeling approachfor describing new product adoption in a competitive market. This model alsodescribes diffusion phenomena in various contexts: infectious disease spreadmodeling and estimation, rumor spread on social networks, prediction ofrenewable energy technology markets, among others. Most of these models,however, consider a deterministic trajectory of the associated state variable(e.g., market-share). In reality, the diffusion process is subject to noise,and a stochastic component must be added to the state dynamics. The stochasticBass model has also been studied in many areas, such as energy markets andmarketing. Exploring the stochastic version of the Bass diffusion model, wepropose in this work an approximation of (stochastic) optimal control surfacesfor a continuous-time problem arising from a $2\times2$ skew symmetricevolutionary game, providing the stochastic counter-part of the Fourier-basedoptimal control approximation already existent in the literature.

Approximation of Optimal Control Surfaces for the Bass Model with Stochastic Dynamics