We study the problem of demand response contracts in electricity markets by quantifying the impact of considering a continuum of consumers with mean–field interaction, whose consumption is impacted by a common noise. We formulate the problem as a Principal–Agent problem with moral hazard in which the Principal—she—is an electricity producer who observes continuously the consumption of a continuum of risk‐averse consumers, and designs contracts in order to reduce her production costs. More precisely, the producer incentivizes each consumer to reduce the average and the volatility of his consumption in different usages, without observing the efforts he makes. We prove that the producer can benefit from considering the continuum of consumers by indexing contracts on the consumption of one Agent and aggregate consumption statistics from the distribution of the entire population of consumers. In the case of linear energy valuation, we provide closed‐form expression for this new type of optimal contracts that maximizes the utility of the producer. In most cases, we show that this new type of contracts allows the Principal to choose the risks she wants to bear, and to reduce the problem at hand to an uncorrelated one.

中文翻译：

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最佳能源需求响应管理的平均场道德风险

我们通过量化考虑均值-场相互作用的连续消费者的影响来研究电力市场中需求响应合同的问题，这些消费者的消费受到共同噪声的影响。我们制定的问题作为委托代理问题与道德风险中的委托-她-是一位电力生产商，他不断观察连续的厌恶风险的消费者的消费量，并设计合同以降低生产成本。更确切地说，生产者激励每个消费者降低其在不同用法中的平均消费量和波动性，而无需观察他所做的努力。我们证明生产者可以通过考虑一个代理的消费合同索引并从整个消费者群体的分布中汇总消费统计信息，从而从考虑消费者的连续性中受益。在线性能源评估的情况下，我们为这种新型的最优合同提供了封闭形式的表达式，以最大化生产者的效用。在大多数情况下，我们表明，这种新型合同允许委托人选择她想承担的风险，