Supply function equilibrium with generation constraints solved through mixed-integer programming

Supply function equilibrium (SFE) developed by Klemperer and Mayer is a popular approach to analyze market power and study gaming strategies in electricity markets. We extend the notion of SFE to the case where power generating companies own multiple generating units with asymmetric generation costs and upper and lower generation limits. Such a SFE is characterized by a set of differential equations subject to inequality constraints which can be expressed as a mixed-integer program (MIP). We then numerically solve and examine the behaviour of affine SFE with generation constraints by solving the defining MIP using standard MIP solvers. The behavior of the affine SFE exhibits enlightening and reasonable results when units switch from (or to) one of their generations limits.