Deregulated electricity market, a stochastic variational approach

On a Class of Multistage Stochastic Hierarchical Problems

“…In view of this result, we focus on the study of a SLMF game of multistage stochastic nature. At the lower-level, the presence of a suitable GNEP of multistage stochastic nature describing the interactions among the followers and parametrized by the leader strategy could allow us to capture a wide range of applications: energy market models, network models, water optimal allocation problems, demand-side management problems, medical supply competitions, etc; see, e.g., [21,23,24,27]. For this reason, this paper is the starting point for future developments.…”

“…Indeed, at the upper level, one can always consider a leader with a certain objective: for instance, it could be a regulator. Instead, at the lower level, it is possible to fit a suitable GNEP describing the interactions among the followers in the considered application, parametrized by the leader strategy; see, e.g., [21,23,24] for problems in multistage stochastic settings.…”

On the study of multistage stochastic vector quasi-variational problems

“…From (20), condition (19) follows. Conversely, if x is a solution to (19), from (i) in Proposition 1, the claim follows.…”

“…Indeed, to capture the dynamics that are essential to stochastic decision processes in response to an increasing level of information, Rockafellar and Wets [27] introduced a multistage stochastic variational problem. This formulation provides innovative and flexible tools to study real-life problems complicated by time, uncertainty, risk and allows us to capture the role of information in the recursive decision processes; see, e.g., [15,20,22,29]. The key concept of this new formulation turns out to be the nonanticipativity: some constraints have to be included in the formulation of the problem to take into account the partial information structure progressively revealed.…”