It is known that Cournot game theory has been one of the theoretical
approaches used more often to model electricity market behavior.
Nevertheless, this approach is highly influenced by the residual demand
curves of the market agents, which are usually not precisely known. This
imperfect information has normally been studied with probability theory,
but possibility theory might sometimes be more helpful in modeling not
only uncertainty but also imprecision and vagueness. In this paper, two
dual approaches are proposed to compute a robust Cournot equilibrium, when
the residual demand uncertainty is modeled with possibility distributions.
Additionally, it is shown that these two approaches can be combined into a
bicriteria programming model, which can be solved with an iterative
algorithm. Some interesting results for a real-size electricity system
show the robustness of the proposed methodology.