|Markets for environmental externalities are typically closely related to the markets causing such externalities, whereupon strategic interaction may result. Along these lines, the market for Green Certificates is strongly interwoven in the electricity market as the producers of green electricity are also suppliers of Green Certificates. In this paper, we formulate an analytic equilibrium model for simultaneously functioning electricity and Green Certificate markets, and focus on the role of market power. We consider two versions of a Nash-Cournot game: a standard Nash-Cournot game where the players treat the market for Green Certificates and the electricity market as separate markets; and a Nash-Cournot game with endogenous treatment of the interaction between the electricity and Green Certificate markets with conjectured price responses. One result is that a certificate system faced with market power may collapse into a system of per unit subsidies, as the producers involved start to game on the joint functioning of markets.