Dynamic access pricing control for fair and stable resource sharing

We consider the co-existence of users with different price sensitivities under dynamic (or surge) pricing that regulates how they access a shared resource.

To balance supply and demand in such settings, some dynamic pricing systems adopt a monotonically increasing price scheme which is well known to be socially regressive, driving out price-sensitive users in favor of price-insensitive ones.

Here, we propose a new dynamic pricing scheme based on a non-monotonic price function that allows all user classes to coexist more fairly when price-insensitive users are present, but automatically reverts to conventional dynamic pricing when they leave the system, even though the exact price-sensitivity composition is unobservable.

The resulting system consists of nonlinear ODEs, which we further investigate to characterize its equilibria and their domains of attraction, first for a single price-sensitive class competing with a price-insensitive one and then for the general $n$-class case.

Numerical simulations demonstrate the effectiveness of the proposed design.