The Price of Anarchy of Two-Buyer Sequential Multiunit Auctions

TL;DR

This paper analyzes the efficiency loss in two-buyer sequential multiunit auctions with complete information, establishing exact and asymptotic bounds on the price of anarchy for general and concave valuation functions.

Contribution

It provides the first precise characterization of the price of anarchy in two-buyer sequential multiunit auctions for general and concave valuations.

Findings

Price of anarchy is exactly 1/T for general valuations with T items.

For concave valuations, the price of anarchy is at least 1 - 1/e (~0.632).

The bound for concave valuations is asymptotically tight as T increases.

Abstract

We study the efficiency of sequential multiunit auctions with two-buyers and complete information. For general valuation functions, we show that the price of anarchy is exactly $1/T$ for auctions with $T$ items for sale. For concave valuation functions, we show that the price of anarchy is bounded below by $1-1/e\simeq 0.632$. This bound is asymptotically tight as the number of items sold tends to infinity.