Risk-Sensitivity in Mean Field Games and Energy Markets

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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.