Price and Capacity Competition
We study the efficiency of oligopoly equilibria in a model where firms compete over capacities and prices. We show that efficiency in the worst oligopoly equilibria can be arbitrarily low. However, if the best oligopoly equilibrium is selected (among multiple equilibria), the worst-case efficiency loss is $$2(\sqrt{N}-1)/(N-1)$$ with $N$ firms, and this bound is tight. We also suggest a simple way of implementing the best oligopoly equilibrium.