Efficiency and Revenue in Linear-Quadratic Double Auctions

We study uniform-price double auctions augmented with a class of subsidy schemes. Using these subsidies, any profile of linear demand schedules can be implemented as an equilibrium outcome. By revenue equivalence, all other mechanisms which implement linear auction equilibria are essentially equivalent to some subsidy scheme in our class. We show that, under a linear dependency condition on primitives, fully efficient, budget balanced, and individually rational trade is possible. Thus, the welfare loss from equilibria in uniform-price auctions without subsidies is a non-fundamental distortion, which can be fixed with better mechanism design. However, we show that monopolist trading platforms have incentives to reduce allocative efficiency to increase revenue, even as the number of traders becomes large.