Compartmental market models in the digital economy—extension of the Bass model to complex economic systems

Compartmental models are widely used in epidemiology, engineering, and physics to describe the temporal behavior of complex systems. This paper presents how compartmental models may be applied to the digital economy—more specifically, how the Bass model can be extended to more complex economics systems such as markets with customer churning, competition, multisided platforms, and online games. It is demonstrated that it is straightforward to establish the equations describing the various economic systems under study, however, the equations are often too complex to be solved analytically in the general case. Though the paper presents simple and idealized cases, the solutions may, nevertheless, uncover important strategic aspects that otherwise may be hidden by complexity in the general case, for example, the reasons for slow initial market growth. The paper also discusses how the developed models may be used to evaluate digital economic market evolution and business policy. •Analytical models that capture competition and churning in digital markets.•How complex digital economic system may be modelled using compartmental models.•How the strength of the network effects impacts market evolution.