Dynamic spatial equilibrium models: an application to the natural gas spot markets

European gas markets have gone through profound restructuring processes in the last 20 years. Directive 98/30/EC represented the first attempt to liberalize this market through the unbundling of gas supply and generation from the operation of transmission networks. The goal of this Directive was the creation of an internal market for gas by breaking up vertically integrated national companies. This commitment to integrate the European gas market was strengthened by Directive 2003/55/EC few years later and then confirmed by the Gas Target Model in 2011. This progressively increasing competition of the European gas market implies significant changes in the pricing system. In particular, it has been envisaged that long-term contracts, traditionally used to trade gas in Europe, could be partially substituted by short-term transactions operated in (liquid) spot markets, possibly organized as implicit auctions. Considering this framework, we investigate the problem of managing a dynamic system of spatially distributed spot markets where gas is traded on an auction basis. These markets are cleared taking into account transmissions, balance, and storage constraints. We propose a set of equilibrium type conditions for this system of markets and show that it is equivalent to a single-level variational inequality problem. In order to find its solution, which yields an equilibrium trajectory, we apply a dual type method. Numerical experiments are conducted on the gas spot markets developed in the Netherlands and in the United Kingdom.