  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.
