We motivate the formulation of market equilibria as a mixed complementarity problem (MCP) in order to bridge the gap between bottom-up energy system models and top-down general equilibrium models for energy policy analysis. Our objective is primarily pedagogic. We first lay out that the MCP approach provides an explicit representation of weak inequalities and complementarity between decision variables and market equilibrium conditions. This permits us to combine bottom-up technological details and top-down economic richness in a single mathematical format. We then provide a stylized example of how to integrate bottom-up features into a top-down modeling framework along with worked examples and computer programs which illustrate our approach.