Strategic Prosumers: How to Set the Prices in a Tiered Market?

We consider users who may have renewable energy harvesting devices or distributed generators. Such users can behave as consumers or producers (hence, we denote them as prosumers) at different time instances. We consider a tieredmarket where the grid selects a price function, which reveals price in the real time based on the total demand to the grid. In the real time, a prosumer can buy from another prosumer in an exchange market knowing the price from the grid. The exchange price is set by a platform and can be different for different sellers. A prosumer is a selfish entity, which selects the amount of energy it wants to buy either from the grid or from other prosumers or the amount of excess energy it wants to sell to other prosumers by maximizing its own payoff. However, the strategy and the payoff of a prosumer inherently depend on the strategy of other prosumers as a prosumer can only buy if the other prosumers are willing to sell. We formulate the problem as a coupled constrained game and seek to obtain the generalized Nash equilibrium. We show that the game is a concave potential game and show that there exists a unique generalized Nash equilibrium. We propose a distributed algorithm that converges to the exchange price, which clears the market and achieves the generalized Nash equilibrium. We, finally, show how the grid should select the price function in a day-ahead scenario by computing the estimated demand from the history. Our numerical result shows that the tiered market can reduce the peak load and increase the prosumers' total payoffs.