This thesis is focused on nonsmooth variational analysis of equilibrium problems with equilibrium constraints. Such an effort is directly motivated by a model of electricity markets encountered in non-cooperative game theory. In such a market there is the so-called Independent System Operator (ISO), a regulator entity that manages the market clearing and the electricity dispatch. This market structure makes the problem of electricity markets challenging from the mathematical point of view. In this area, we discovered several possibilities for further development.First, the best responses of producers in a speci c variant of a model is fully analysed. This progress was due to an analytical formula for a unique solution to the lower level ISO problem, which is one of the main contributions of the author of this thesis. Then, for a more general model of the market, stability of the so-called M(ordukhovich)-stationarity points is provided based on the concept of coderivatives. To this end, the respective second order limiting coderivative was computed by the author of this thesis. Finally, the concept of limiting normal operator is proposed, a new tool for quasiconvex analysis exhibiting workable calculus rules. The basic idea coming from the author of this thesis is to employ the same limiting construction that is used in modern variational analysis in connection with normal cones to sets. This topic is motivated by the classical assumption in many non-cooperative games where the loss function of players is often assumed to be quasiconvex.