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.

When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness). We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann O’Callaghan, and Shoham, who presented greedy heuristics. We show how to use IF-THEN-ELSE constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios. 1

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We study auctions with severe bounds on the communication allowed: each bidder may only transmit t bits of information to the auctioneer. We consider both welfare-maximizing and revenuemaximizing auctions under this communication restriction. For both measures, we determine the optimal auction and show that the loss incurred relative to unconstrained auctions is mild. We prove non-surprising properties of these kinds of auctions, e.g. that discrete prices are informationally ecient, as well as some surprising properties, e.g. that asymmetric auctions are better than symmetric ones.

Secure Distributed Computing addresses the problem of performing a computation with a number of mutually distrustful participants, in such a way that each of the participants has only limited access to the information needed for doing the computation. Over the past decade, a number of solutions for this problem have been developed. The various proposed solutions dier in the cryptographic primitives that are used, and in the class of computations that can be performed. However, all su- ciently general solutions have one thing in common: the communication overhead between the involved parties seems to be prohibitive. In this paper, we consider a concrete instance (with considerable practical interest) of the general problem of secure distributed computing, and we investigate how bad the communication overhead really is. This involves tailoring the dierent general solutions to the specic problem at hand, optimizing them for minimal communication overhead, and evaluating the resulting ...

Secure distributed computing addresses the problem of performing a computation with a number of mutually distrustful participants, in such a way that each of the participants has only limited access to the information needed for doing the computation. Over the past two decades, a number of solutions requiring no trusted third party have been developed using cryptographic techniques. The disadvantage of these cryptographic solutions is the excessive communication overhead they incur. In this paper, we use one of the SDC protocols for one particular application: second price auctions, in which the highest bidder acquires the item for sale at the price of the second highest bidder. The protocol assures that only the name of the highest bidder and the amount of the second highest bid are revealed. All other information is kept secret (the amount of the highest bid, the name of the second highest bidder, ...). Although second price auctions may not seem very important, small variations on this theme are used by many public institutions: e.g., a 1 2 call for tenders, where contract is given to the lowest oer (or the second lowest). The case study serves two purposes: we show that SDC protocols can be used for these kind of applications, and secondly, we assess the network overhead and how well these applications scale. To overcome the communication overhead, we use mobile agents and semi-trusted hosts. Keywords: Secure distributed computing, SDC, mobile agents, second price auction, agents, semi-trusted execution platform 1.