Parameterized supply function equilibrium in power networks

We consider the setting in which generators compete in scalar-parameterized supply functions to serve an inelastic demand spread throughout a transmission constrained power network. The market clears according to a locational marginal pricing mechanism, in which the independent system operator (ISO) determines the generators' production quantities so as to minimize the revealed cost of meeting demand, subject to transmission and generator capacity constraints. Under the assumption that both the ISO and generators choose their strategies simultaneously, we establish the existence of Nash equilibria for the underlying game, and derive a tight bound on its price of anarchy. Under the more restrictive setting of a two-node power network, we present a detailed comparison of market outcomes predicted by the simultaneous-move formulation of the game against those predicted by the more plausible sequential-move formulation, where the ISO observes the generators' strategy profile prior to determining their production quantities.