The Utility Competition, Price Competition and Quantity Competition

We propose a framework of utility competition (UC), and we provide the intuition why price competition (PC), quantity competition (QC) and UC differ, and prove it by using a nonlinear demand system. If the network externality is positive, then PC is the most efficient with the lowest equilibrium price, QC is the least efficient, and UC is in the middle. While if the externality is negative, then UC is the most efficient with the lowest equilibrium price, QC is still the least efficient, and PC is in the middle. We also rank the profits