An energy market model can contain binary variables, typically to represent on/off or build/don't build decisions. I consider a definition of equilibrium for models with continuous and binary variables, and an algorithm that is guaranteed to find an equilibrium if one exists. I consider alternative models that can have solutions even when the usual model does not. The equilibrium definition and algorithm can be applied to competitive or Nash-Cournot models, and to single commodity or multicommodity models. As far as I know, all previous equilibrium models with continuous and integer variables were based on the notion that market equilibrium tends to maximize social welfare. Therefore, previous "mixed integer" equilibrium models could not even be formulated for Nash-Cournot or multicommodity settings (except with severely limiting assumptions). I discuss the relationship between social welfare maximization and the new equilibrium definition. Some simple illustrative models will be presented to motivate the general results.
Groupe d’études et de recherche en analyse des décisions