Truth revelation in approximately efficient combinatorial auctions

TLDR

Classical mechanisms in microeconomics and game theory, such as combinatorial auctions and the Generalized Vickrey Auction, rely on solving difficult optimization problems that are typically only approximated in practice, challenging traditional truth‑revelation analyses. We examine how replacing exact optimization solutions with approximate ones affects the truth‑revelation properties of these mechanisms. We analyze a greedy optimization method and propose an alternative payment scheme that guarantees truthfulness for a restricted class of players. Our results show that the GVA payment scheme fails to ensure truth‑revelation, whereas the proposed scheme achieves dominant‑strategy truthfulness under natural auction properties that extend beyond the studied auction.

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.