Principal-agent problems, contract theory and mean-field games for energy – PACMAN

On the mathematical side, we propose to tackle three main challenges. Contract theory which analyses interactions between agents with asymmetric information is the first challenge. It will bring mathematical insights for the three applications of the project. The main milestones are the extension of the literature to treat energy applications (premature contract termination, limited liabilities of agents, uncertainties on production or consumption), the understanding of how adverse selection interacts with with moral hazard, and the development of efficient numerical methods handling non-Markovian features. Mean-field game theory which is devoted to the analysis of differential games with a large number of small players in interaction is the second challenge. It enables to tackle principally the second and third applications listed above, i.e. investment and behaviours in energy markets, like new technology spreading. The main milestones are the development of volatility control in mean-field games (highly important for efficient consumption control), then the exploration of the link between contract theory and mean-field games, and finally the development of efficient numerical methods in relation with the first challenge. The last challenge in behavioural economics will improve the realism and the applicability of the models we will develop. In particular, the time-inconsistency of consumers needs to be represented to propose correct tariff schemes or incentives. The main milestones are: the development of time-inconsistent stochastic control in particular in non- Markovian settings, and the introduction of behavioural preferences in principal-agent problems.

«
The privileged partnership around this project with EDF has enabled us to make significant progress on the following applications
- The establishment of optimal tariffs for the sale of electricity through Principal-Agent models including adverse selection
- Energy precariousness and insurance design
- The impact of electricity pricing on the development of individual batteries in the electrical system
This work served to shed light on EDF's public service mission and to work on new topics to provide optimization methods for the establishment of a public-use rate. The continuation of our projects allowed the elaboration of a patent carried by members of the consortium entitled ««««Procédé de gestion des contraintes de flexibilité d’un système production-consommation d’électricité par le contrôle de la variance de la consommation««. International research partnerships have been developed through the project, notably in Singapore, the USA and Chile. In particular, we are currently establishing close links with local companies in Chile on powergrid management and renewable energy issues.«

«The project coordinator received the 2017 Young researcher prize in Finance and Insurance of the Europlace Institute of Finance and was a plenary speaker at the Second conference on the mathematics of energy markets, Wolfgang Pauli institute, Vienna, Austria, July 2017.
The summer school of the ANR project took place in August 2018 at the Ecole Polytechnique in Palaiseau, France, during the 11th European Summer School in Financial Mathematics.
Several conferences and events have or will be funded and/or organized by the ANR project: in China, in May 2017, in Hammamet, Tunisia, in October 2017 and October 2018, in Santiago, Chile, in March 2018.
All thes event have been wonderful opportunities to disseminate the results and progresses of the project members.«

«1 patent filed, 22 articles published during the project in international refereed journals, and 12 artickes in preparation. Several conferences organised, as well as a summer school targeting young PhD students. Major articles: - Alasseur, C., Ekeland, I., E´lie, R., Herna´ndez Santiba´n~ez, N., Possamai¨, D. (2017). An adverse selection approach to power pricing, arXiv:1706.01934.
- Cvitanic´, J., Possamai¨, D., Touzi, N. (2018). Dynamic programming approach to principal-agent problems, Finance and Stochastics, 22(1):1-37.
- El Euch, O., Mastrolia, T., Rosenbaum, M., Touzi, N. (2018). Optimal make-take fees for market making regulation, arXiv:1805.02741.«

The main objective of this research project is to understand from regulators, energy producers and providers’ perspectives, how to optimise tariff structure, risk sharing, subsidy policies, and to promote efficient investments in the energy sector. Our project is structured around three applications. First, we will focus on consumption management, energy efficiency and demand response. Indeed, one may improve renewable development by dealing with demand and production, to avoid costly expenses. This methodology is already advanced but the development of smart meters allows to extend it further, and to design better tariff structures with respect to consumers' reactions and competitor’s offers. The second one is concerned with investments, which are a main challenge in the energy sector, since they have to guaranty quality of service, security, and EU objectives in term of green energy and emission reduction. Optimized energy tariffs could enable risk sharing between producers and consumers and promote optimal investment. Our last application is devoted to model agents’ behaviours in energy markets, especially non-rational ones like time-inconsistency (adoption of new technologies, public helps for energy bills, tariffs to avoid non-rational change of contracts by consumers).

On the mathematical side, the modelling of these types of questions has been studied notably by members of the project. Still, many issues remain open for concrete applications and exploitable policies. We propose to tackle three main challenges. First, contracting theory which analyses interactions between agents with asymmetric information structure. It will bring mathematical insights for the three applications of the project. Main milestones are extension of literature to treat energy applications (end contract prematurely, added constraints like limited liabilities of agents, include uncertainties on production or consumption), understanding how adverse selection setting can be incorporated with moral hazard, and development of efficient numerical methods handling non-Markovian features. Second, mean field game theory which is devoted to the analysis of differential games with lots of small players in interaction. It enables to tackle principally applications 2 and 3 listed above, i.e. investment and behaviours in energy markets, like new technology spreading. Main milestones are first the development of volatility control in mean-field games (highly important for efficient consumption control), then the exploration of the link between contracting theory and mean-field games, and third the development of efficient numerical methods with cooperation with first challenge. The last challenge in behavioural economics will improve the modelling of all applications we are studying. In particular, time-inconsistency of consumers needs to be represented to propose correct tariff schemes or incentives. Main milestones are: develop time-inconsistent stochastic control in particular in non-Markovian settings, and add behavioural preferences in principal-agent problems.

This project aims at breakthroughs in the realistic modelization of behaviours in energy markets to provide an efficient help to the players in the energy market, in terms of decision-making. We want to not only use innovative theories to understand how players optimally act, we also want to understand how they interact and take into account the fact that most of them are not perfect rational Homo œconomicus. This is an unprecedented effort that we are convinced we can achieve by bringing together not only specialists in these questions in both the mathematics and economics academic spheres, but also a key player of the French electricity market, namely EDF. Our results will be disseminated through several conferences opened to the academic and industrial worlds, patents (one is already being prepared), international collaborations and publications of our results in scientific journals.