Risk-Sensitivity in Mean Field Games and Energy Markets

动机：由于全球变暖，有必要在全球范围内减少碳排放。有鉴于此，已经实施了监管法案，要求受监管的公司通过合格的可再生能源产生特定比例的电力。通过为每1兆瓦时的可再生能源发电颁发证书，有一个跟踪系统。如果不遵守规定，这些公司将面临必须向监管机构支付的罚款。这些证书可以在市场上交易，其价格由供求关系驱动。由于间歇性可再生能源的不确定性，价格可能非常波动，在这种市场上进行交易可能会给公司带来更高的风险。此外，这类市场的交易成本一般高于自愿市场。因此，为了促进监管，从而有助于更顺利地向低碳未来过渡，有效的市场设计至关重要。 目的：平均场博弈（Mean Field Game，MFG）理论研究的是一类大种群博弈，在这种博弈中，智能体不仅受到个体行为的影响，还受到系统中所有其他智能体的集体行为的影响。该理论提供了这类博弈的纳什均衡的数学描述。本提案的目的是对制造业集团的风险敏感性进行基本研究，并将其用于合规REC市场的最佳设计。因此，本提案的第一部分研究了参与者对风险敏感且存在有影响力的市场参与者的市场中的均衡定价和合同设计。在所有的分析中，假设所有的市场参数都是已知的，就像游戏中通常的情况一样。然而，后一种假设在实践中并不成立，需要某种形式的学习。因此，在第二部分中，研究了MFG中个体和群体参数的风险敏感学习。这为在每个案例中为合规市场案例研究提出的广泛的数据驱动分析铺平了道路，最终将用于市场设计目的。本提案中考虑的设置在文献中未提及。更具体地说，这包括考虑制造业的风险敏感性，以实现均衡定价、合同设计、对有影响力的市场参与者（主要代理人）进行建模以及学习和适应。 方法学：本提案中的一系列项目涉及制造业风险敏感性的不同方面，其设计方式是可以同时和相互独立地进行调查。在所有项目中使用的主要分析工具是MFG方法，该方法已被证明在模拟具有大量交互参与者和少数有影响力的参与者的市场时非常有用。我们扩展的方法来考虑风险敏感性的代理商在市场上的清算条件，风险敏感的主要代理商，和风险敏感的学习和适应。

Motivation: Due to global warming, it is necessary to reduce carbon emissions worldwide. In this light, regulatory acts have been imposed by requiring the regulated firms to generate a specific percentage of their electricity via an eligible renewable energy resource. There is a tracking system via issuing certificates for every 1 MWh renewable energy generation. In case of non-compliance, the firms face a monetary penalty that must be paid to the regulator. These certificates can be traded on markets and their price is driven via supply and demand. Due to the uncertainty associated with intermittent renewables, the price could be very volatile and trading in such markets could incur a higher risk to firms. Moreover, transaction costs in such markets are in general higher than in voluntary markets. Hence, to facilitate the regulation, which in turn contributes to a smoother transition to a low-carbon future, an efficient market design is crucial. Objective: Mean field game (MFG) theory studies a class of large-population games, where agents are not only impacted by their individual behaviour but also by the mass behaviour of all the other agents in the system. The theory provides mathematical characterizations of the Nash equilibria of such games. The objective of this proposal is to introduce a fundamental study of risk-sensitivity in MFGs and to employ it for optimal design of compliance REC markets. Therefore, the first part of this proposal investigates equilibrium pricing and contract design in markets where participants are risk sensitive and there is an influential market participant. In all analyses it is assumed that all market parameters are known as is usually the case in games. However, the latter assumption does not hold in practice and some form of learning is required. For that reason, in the second part, risk-sensitive learning of the individual and the population parameters in MFGs is investigated. This paves the way for extensive data-driven analysis proposed in each case for compliance markets case studies, which ultimately will be used for market design purposes. The setups considered in this proposal are not addressed in the literature. More specifically, this, among others, includes considering risk-sensitivity in MFGs for equilibrium pricing, contract design, modeling an influential market participant (major agent), and learning and adaptation. Methodology: The set of projects in this proposal addresses different aspects of risk-sensitivity in MFGs and is designed in a way that they can be investigated simultaneously and independently of each other. The main analytical tool that is used in all projects is MFG methodology which has proven useful in modeling markets with a large number of interacting participants and a few influential ones. We extend the methodology to account for risk-sensitivity of agents in markets with a clearing condition, a risk-sensitive major agent, and risk-sensitive learning and adaptation.