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"Market Coupling'' is currently seen as the most advanced market design in the restructuring of the European electricity market. Market coupling, by construction, introduces what is generally referred to as an incomplete market: it leaves several constraints out of the market and hence avoids pricing them. This may or may not have important consequences in practice depending on the case on hand. Quasi-VariationalInequality problems and the associated Generalized Nash Equilibrium can be used for representing incomplete markets. Recent papers propose methods for finding a set of solutions of Quasi-Variational Inequality problems. We apply one of these methods to a subproblem of market coupling namely the coordination of counter-trading. This problem is an illustration of a more general question encountered for instance in hierarchical planning in production management. We first discuss the economic interpretation of the Quasi-Variational Inequality problem. We then apply the algorithmic approach to a set of stylized case studies in order to illustrate the impact of different organizations of counter-trading. The paper emphazises the structuring of the problem. A companion paper considers the full problem of market coupling and counter-trading and presents a more extensive numerical analysis.

Loyola de Palacio Programme on Energy Policy Cross-border trade remains a contentious issue in the restructuring of the European electricity market. Difficulties stem from the lack of a common market design, the separation between energy and transmission markets and the insufficient coordination between Transmission System Operators (TSOs). This paper analyzes the cross-border trade problem through a set of models that represent different degrees of coordination both between the energy and transmission markets and among national TSOs. We first present the optimal organisation, not implemented in Europe, where energy and transmission are integrated according to the nodal price paradigm and Power Exchanges (PXs) and Transmission System Operators (TSOs) are integrated. This is our reference case. We then move to a more realistic representation of the European electricity market based on the so-called marketcoupling design where energy and transmission are operated separately by PXs and TSOs. When considering different degrees of coordination of the national TSOs' activities, we unexpectedly find that some arrangements are more efficient than the lack of coordination might suggest. Specifically we find that even without a formal coordination of the TSOs' counter-trading operations, non discriminatory access to common counter-trading resources for all TSOs may lead to a partial implicit coordination of these TSOs. In other words, an internal market of counter-trading resources partially substitutes the lack of integration of the TSOs. While a full access to counter-trading resources is a weaker requirement than the horizontal integration of the TSOs, it is still quite demanding. We show that quantitative limitations to the access of these resources decrease the efficiency of counter-trading. The paper supposes price taking agents and hence leaves aside the incentive to game the system induced by zonal systems.