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Consider an electricity market populated by competitive agents using thermal generating units. Such generation involves the emission of pollutants, on which a regulator might impose constraints. Transmission capacities for sending energy may naturally be restricted by the grid facilities. Both pollution standards and transmission capacities can impose several constraints upon the joint strategy space of the agents. We propose a coupled constraints equilibrium as a solution to the regulator’s problem of avoiding both congestion and excessive pollution. Using the coupled constraints’ Lagrange multipliers as taxation coefficients the regulator can compel the agents to obey the multiple constraints. However, for this modification of the players’ payoffs to induce the required behaviour a coupled constraints equilibrium needs to exist and must also be unique. A three-node bilateral market example with a DC model of the transmission line constraints described in [2] possesses these properties and will be used in this paper to discuss and explain the behaviour of the agents subjected to coupled constraints.