Energy markets are complex networks of producers, exporters, traders and consumerscharacterized by different market structures in each sector. The infrastructuralnetwork connecting the markets plays an important role in determining thevolume of the trade flows and the location of the final consumption.The market players’ behavior in an energy market can be described using a gametheoretic approach where each player’s decision depends on the other market playersdecisions. Over the last decades these ideas have evolved and there have beenproduced some material where markets for a single commodity are modeled, usingideas from game theory to describe the players’ influence on each other’s decisions.However, little work has been done analyzing multi-commodity markets with thesame set of tools. Based on existing literature that is written on single-commoditymodeling, we have applied equilibrium programming with complementarity structureto describe the markets for electricity and natural gas in Northern Europethrough a strategic market model. The complexity level is potentially high, so wedecided to limit ourselves to a deterministic and myopic model without investmentpossibilities.The problem is formulated through a strategic MCP model where each marketparticipant solves an optimization problem connected through the market clearingconditions. Besides showing that the model is an MCP we implemented the modelin GAMS and solved it for the gas and electricity market in Northern Europe.Our results indicates that a Cournot model gives an adequate description of theelectricity and gas market in Northern Europe, and that considerable changes inproduction, consumption, traded volumes and prices in one market can lead toprice, quantity and welfare effects in markets far away from the initial cause. Wecan also register close links between the markets for electricity and natural gas,suggesting that agents’ behavior in one commodity market might affect the othercommodity market and vice versa.