The economic efficiency of simple pricing mechanisms in two-sided markets

We study the price of anarchy of a simple budget-balanced trading mechanism for multiple divisible goods in markets containing both producers and consumers (i.e. two-sided markets). Each producer is asked to submit a linear pricing function that specifies a per-unit price p(d) as a function of the demand d that it faces. Consumers then buy their preferred resource amounts at these prices. We prove that having three producers for every resource guarantees the price of anarchy is bounded. In general, the price of anarchy depends heavily on the level of horizontal and vertical competition in the market, on producers’ cost functions, and on the elasticity of consumer demand. We show how these characteristics affect economic efficiency and in particular, we find that the price of anarchy equals 2/3 in a perfectly competitive market, 3/4 in a monopsony, and 2 (2− )/(4− ) in a monopoly where consumer valuations have a fixed elasticity of . These results hold in markets with multiple goods, particularly in bandwidth markets over arbitrary graphs. Variants of this mechanism have been commercially deployed in the past; our results suggest how to modify these systems, so that they are provably efficient. On the theory side, our work demonstrates that nearoptimal efficiency can be achieved within two-sided markets by very simple and natural pricing mechanisms. It also generalizes several results for fixed-demand and fixed-supply markets.