A Bertrand model with Brownian motion and behavioral errors

This paper extends a random version of Bertrand model with Brownian motion. The model can be used to adjust price with changing economic environment, as it can serve to capture the behaviours of managers who seek to avoid errors in identifying the optimal response in dynamic price settings within their respective markets. The equilibrium of a stochastic game model is further discussed with the solution solved by Hamilton-Jacobi-Bellman equations, and the equilibrium exhibited fluctuations in the numerical simulation, with a constant value being observed. Finally, the model shows that organisations that are less efficient at managing errors, particularly those with a smaller market share, are more susceptible to failure.