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In this paper, the problem of smart grid energy management under stochasticdynamics is investigated. In the considered model, at the demand side, it isassumed that customers can act as prosumers who own renewable energy sourcesand can both produce and consume energy. Due to the coupling between theprosumers' decisions and the stochastic nature of renewable energy, theinteraction among prosumers is formulated as a stochastic game, in which eachprosumer seeks to maximize its payoff, in terms of revenues, by controlling itsenergy consumption and demand. In particular, the subjective behavior ofprosumers is explicitly reflected into their payoff functions using prospecttheory, a powerful framework that allows modeling real-life human choices. Forthis prospect-based stochastic game, it is shown that there always exists astationary Nash equilibrium where the prosumers' trading policies in theequilibrium are independent of the time and their histories of the play.Moreover, a novel distributed algorithm with no information sharing amongprosumers is proposed and shown to converge to an $\epsilon$-Nash equilibrium.On the other hand, at the supply side, the interaction between the utilitycompany and the prosumers is formulated as an online optimization problem inwhich the utility company's goal is to learn its optimal energy allocationrules. For this case, it is shown that such an optimization problem admits ano-regret algorithm meaning that regardless of the actual outcome of the gameamong the prosumers, the utility company can follow a strategy that mitigatesits allocation costs as if it knew the entire demand market a priori.Simulation results show the convergence of the proposed algorithms to theirpredicted outcomes and present new insights resulting from prospect theory thatcontribute toward more efficient energy management in the smart grids.

Stochastic Games for Smart Grid Energy Management with Prospect Prosumers