# Stochastic Games for Smart Grid Energy Management with Prospect Prosumers

arXiv: https://arxiv.org/abs/1610.02067 · HTML: https://mlsanity.com/paper/1610.02067/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2016.

## Built on by (most cited first, 6 of 6)

- [Learning Stationary Nash Equilibrium Policies in n-Player Stochastic Games with Independent Chains](https://mlsanity.com/paper/2201.12224/) (2022)
- [Scalable and Independent Learning of Nash Equilibrium Policies in n-Player Stochastic Games with Unknown Independent Chains](https://mlsanity.com/paper/2312.01587/) (2023)
- [Independent Learning of Nash Equilibria in Partially Observable Markov Potential Games with Decoupled Dynamics](https://mlsanity.com/paper/2605.06377/) (2026)
- [Policy Optimization and Multi-agent Reinforcement Learning for Mean-variance Team Stochastic Games](https://mlsanity.com/paper/2503.22779/) (2025)
- [Independent policy gradient-based reinforcement learning for economic and reliable energy management of multi-microgrid systems](https://mlsanity.com/paper/2511.20977/) (2025)
- [Fully Online Decentralized Learning in Stochastic Games with Unknown Independent Chains](https://mlsanity.com/paper/2610.01181/) (2026)

## Abstract (arXiv)

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