Abstract
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, while ensuring that transmission and generator capacity constraints are met. Under the stylizing assumption that both the ISO and generators choose their strategies simultaneously, we establish the existence of Nash equilibria for the underlying market, and derive a tight bound on its price of anarchy (PoA). In addition to providing a structural characterization of a generator's market power, the PoA bound we derive reveals the possibility of a Braess paradox - that is to say, the strengthening of a network's transmission capacity can lead to an increase in the total cost of generation at a Nash equilibrium.
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