Principal-Agent, Contracts and Mean-field gAmes for eNergy (PACMAN)



Our aim is to understand the public policies and business practices that will offer the best perspectives for adequate investment and quality of services in the energy sector. The complex interactions between individual players, firms, and regulators require a huge scientific effort from complementary academic disciplines. The interest in these questions is not new. We have ranked priorities based on our analysis of the domain and we have identified where we think research could be most effective. Our project is structured around three main applications. The first one is consumption management, in particular energy efficiency and demand response. This is where lies the bulk of potential improvement in energy use. The business-as-usual critique of renewable energy is based on a purported inadequacy with demand. In fact, adequacy could be approached: the variability of renewable production could be handled by consumption management schemes, some purely technological, others based on well-designed tariffs and powerful incentives. The development of smart meters for example is a big step in that direction, yet the way they will be actually used will make all the difference, and research is needed to achieve that goal. Moreover, the energy sector is competitive at all levels. In that context, the implementability of the solutions must be considered from the start. Investment is a big challenge in the energy sector since it is the basis to guarantee the quality of service and security, and also the fulfilment of EU objectives in terms of green energy and emission reduction. Our second application is focused on that fundamental issue: improving investment. Indeed, optimized energy tariffs could contain a better risk sharing between producers and consumers. Provided this sharing is really based on abilities to bear risk, investment could be optimized. In addition, the organisation of the market will be investigated. Indeed, the interactions between regulator, producers, and retailers are the conditions of success or failure. Our last application is devoted to model actual behaviours in energy markets, in the line of the behavioural economics methodologies, at least for consumers. Time inconsistency and more generally the misunderstanding of long term benefits are notions well documented in the empirical literature. The consequences for regulation and incentives in the domain of energy have to be drawn. We intend to provide useful models for policy-makers and managers along these lines. Direct applications are the adoption of new technologies, social tariffs implemented via subsidized prices or coupons, legibility of tariffs by consumers. Many of these problems are well-known but have not been subjected to a systematic analytical effort.
On the mathematical side, the modelling of tightly related questions has been studied by members of the project. Still, many issues remain open for concrete applications and exploitable policies. 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. To make breakthroughs in the realistic modelling of behaviours in the energy market, we will not only use innovative theories of optimal behaviour, we will also innovate in the modelling of interaction, keeping in view that players are not the perfectly rational homo oeconomicus. Indeed, modelling improvement is a key factor for business sector and policy makers to adopt the models we will develop. This is an  nprecedented collaborative effort. We bring together not only specialists in these questions from the mathematics and economics academic spheres, but also a key player of the French electricity market, namely EDF. Our results will be disseminated through conferences opened to the academic and industrial worlds, patents (one is already being prepared), international collaborations and publications of our results in scientific journals, and up-to-date teaching and student supervision.


Project : 01/10/2016 – 30/09/2021


Contact in TSE : Stéphane Villeneuve