Game-Theoretic Energy Source Allocation Mechanism in Smart-Grids

Abstract: This work studies the decentralized and uncoordinated energy source selection problem for smart-grid consumers with heterogeneous energy profiles and risk attitudes: they compete for a limited amount of renewable energy in their local community, at the risk of paying a higher cost if that energy is not enough to supply all such demand. We model this problem as a non-cooperative game and study the existence of mixed-strategy Nash equilibria (NE) under the proportional allocation policy employed when the total demand for renewable energy exceeds the available one. We derive under NE closed-form expressions for the resulting total renewable energy demand and social cost under varying consumer profiles, energy costs and availability. The analysis also provides useful guidelines as to what consumers should do (compete or not) based on their risk attitude or if they should be more risk-taking, under certain conditions. Finally, we study numerically the efficiency of this decentralized scheme compared to a centralized one via the price-of-anarchy metric.