Quasi-Proportional Mechanisms: Prior-free Revenue Maximization

TL;DR

This paper introduces quasi-proportional auction mechanisms for single-item allocation that are simple, prior-free, and guarantee pure Nash equilibria, with promising revenue bounds demonstrated analytically and experimentally.

Contribution

It proposes a new class of quasi-proportional allocation mechanisms, proving equilibrium existence, uniqueness, and providing polynomial-time computation methods.

Findings

Pure Nash equilibria exist and are unique for the proposed mechanisms.

The mechanisms achieve high revenue compared to the highest bidder value.

Analytical and experimental bounds on revenue demonstrate the mechanisms' effectiveness.

Abstract

Inspired by Internet ad auction applications, we study the problem of allocating a single item via an auction when bidders place very different values on the item. We formulate this as the problem of prior-free auction and focus on designing a simple mechanism that always allocates the item. Rather than designing sophisticated pricing methods like prior literature, we design better allocation methods. In particular, we propose quasi-proportional allocation methods in which the probability that an item is allocated to a bidder depends (quasi-proportionally) on the bids. We prove that corresponding games for both all-pay and winners-pay quasi-proportional mechanisms admit pure Nash equilibria and this equilibrium is unique. We also give an algorithm to compute this equilibrium in polynomial time. Further, we show that the revenue of the auctioneer is promisingly high compared to the ultimate, i.e., the highest value of any of the bidders, and show bounds on the revenue of equilibria both analytically, as well as using experiments for specific quasi-proportional functions. This is the first known revenue analysis for these natural mechanisms (including the special case of proportional mechanism which is common in network resource allocation problems).