Truth Revelation in Approximately Efficient Combinatorial Auctions

TL;DR

This paper examines how approximate solutions in combinatorial auctions affect truthfulness, showing that standard payment schemes may fail and proposing alternative schemes that ensure truthfulness for certain players.

Contribution

It introduces a new payment scheme that guarantees truthfulness in combinatorial auctions when only approximate solutions are feasible, extending the understanding of mechanism design under computational constraints.

Findings

GVA payment scheme does not ensure truthfulness with approximate solutions

A new payment scheme guarantees truthfulness for a restricted class of players

Identifies natural properties that imply truthfulness in combinatorial auctions

Abstract

Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a difficult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard for combinatorial auctions, the Generalized Vickrey Auction (GVA). Traditional analysis of these mechanisms - in particular, their truth revelation properties - assumes that the optimization problems are solved precisely. In reality, these optimization problems can usually be solved only in an approximate fashion. We investigate the impact on such mechanisms of replacing exact solutions by approximate ones. Specifically, we look at a particular greedy optimization method. We show that the GVA payment scheme does not provide for a truth revealing mechanism. We introduce another scheme that does guarantee truthfulness for a restricted class of players. We demonstrate the latter property by identifying natural properties for combinatorial auctions and showing that, for our restricted class of players, they imply that truthful strategies are dominant. Those properties have applicability beyond the specific auction studied.