Walrasian equilibrium power allocation in protected and shared bands

We consider two transmitter-receiver pairs (links) operating on protected and shared frequency bands. Each link has a frequency band to use exclusively without any interference from the other link. A frequency band is shared between the two links. We study the power allocation problem of the two transmitters in the available bands using models from microeconomic theory. We model the setting as a competitive market in which the links are the consumers and transmission power are goods which can be bought by the consumers at specific prices. We assume there exists an authority, the arbitrator, which determines the prices of the goods and forwards them to the consumers. The Walrasian equilibrium in this model is Pareto optimal and corresponds to the prices that equate the demand to the supply of goods. We show that the Walrasian equilibrium always exists in our setting. We provide sufficient conditions for the uniqueness of the Walrasian equilibrium and also for the global stability of the price adjustment process to reach the equilibrium.