With the advent of prosumers, the traditional centralized operation may become impracticable due to computational burden, privacy concerns, and conflicting interests. In this article, an energy sharing mechanism is proposed to accommodate prosumers’ strategic decision-making on their self-production and demand in the presence of capacity constraints. Under this setting, prosumers play a generalized Nash game. We prove main properties of the game: an equilibrium exists and is partially unique; no prosumer is worse off by energy sharing and the price-of-anarchy is $1-O(1/I)$ where $I$ is the number of prosumers. In particular, the PoA tends to 1 with a growing number of prosumers, meaning that the resulting total cost under the proposed energy sharing approaches social optimum. We prove that the corresponding prosumers’ strategies converge to the social optimal solution as well. Finally we propose a bidding process and prove that it converges to the energy sharing equilibrium under mild conditions. Illustrative examples are provided to validate the results.

中文翻译：

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通过能量共享和融合证明来实现生产者社会最优

随着生产者的出现，由于计算负担，隐私问题和利益冲突，传统的集中式操作可能变得不切实际。在本文中，提出了一种能量共享机制，以在存在容量限制的情况下满足生产者自身生产和需求的战略决策。在此设置下，生产者将玩广义Nash游戏。我们证明了游戏的主要特性：均衡存在并且部分是唯一的；能源共享不会使生产者变得更糟，无政府状态的价格是 $ 1-O（1 / I）$ 在哪里 $ I $ 是生产者的数量。特别是，随着越来越多的生产者，PoA趋于1，这意味着在提议的能量共享下所产生的总成本接近社会最优。我们证明了相应的生产者的策略也收敛于社会最优解。最后，我们提出了一个投标过程，并证明了它在温和条件下收敛到能量共享平衡。提供了说明性示例以验证结果。