An Approximate Truthful Mechanism for Combinatorial Auctions with Single Parameter Agents

Abstract

Mechanism design seeks algorithms whose inputs are provided by selfish agents who would lie if it were to their advantage. Incentive-compatible mechanisms compel the agents to tell the truth by making it in their self-interest to do so. Often, as in combinatorial auctions, such mechanisms involve the solution of NP-hard problems. Unfortunately, approximation algorithms typically destroy incentive compatibility. Randomized rounding is a commonly used technique for designing approximation algorithms. We devise a version of randomized rounding that is incentive-compatible, giving a truthful mechanism for combinatorial auctions with single parameter agents (e.g., "single minded bidders'') that approximately maximizes the social value of the auction. We discuss two orthogonal notions of truthfulness for a randomized mechanism---truthfulness with high probability and in expectation---and give a mechanism that achieves both simultaneously.

We consider combinatorial auctions where multiple copies of many different items are on sale, and each bidder i desires a subset $S_i$. Given a set of bids, the problem of finding the allocation of items that maximizes total valuation is the well-known SetPacking problem. This problem is NP-hard, but for the case of items with many identical copies, the optimum can be approximated very well. To turn this approximation algorithm into a truthful auction mechanism, we overcome two problems: We show how to make the allocation algorithm monotone, and give a method to compute the appropriate payments efficiently.