Analysis of Energy Markets Modeled as Equilibrium Problems with Equilibrium Constraints

Equilibrium problems with equilibrium constraints are challenging both theoretically and computationally. However, they are suitable/adequate modeling formulations in a number of important areas, such as energy markets, transportation planning, and logistics. Typically, these problems are characterized as bilevel Nash-Cournot games. For instance, determin- ing the equilibrium price in an energy market involves top-level decisions of … Read more


We examine how different pricing frameworks deal with nonconvex features typical of day-ahead energy prices when the power system is hydro-dominated, like in Brazil. For the system operator, requirements of minimum generation translate into feasibility issues that are fundamental to carry the generated power through the network. When utilities are remunerated at a price depending … Read more

An approximation scheme for a class of risk-averse stochastic equilibrium problems

We consider two models for stochastic equilibrium: one based on the variational equilibrium of a generalized Nash game, and the other on the mixed complementarity formulation. Each agent in the market solves a one-stage risk-averse optimization problem with both here-and-now (investment) variables and (production) wait-and-see variables. A shared constraint couples almost surely the wait-and-see decisions … Read more

A Class of Dantzig-Wolfe Type Decomposition Methods for Variational Inequality Problems

We consider a class of decomposition methods for variational inequalities, which is related to the classical Dantzig–Wolfe decomposition of linear programs. Our approach is rather general, in that it can be used with set-valued or nonmonotone operators, as well as various kinds of approximations in the subproblems of the functions and derivatives in the single-valued … Read more