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.

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This paper deals with multi-unit combinatorial auctions where there are n types of goods for sale, and for each good there is some fixed number of units. We focus on the case where each bidder desires a relatively small number of units of each good. In particular, this includes the case where each good has exactly k units, and each bidder desires no more than a single unit of each good. We provide incentive compatible mechanisms for combinatorial auctions for the general case where bidders are not limited to single minded valuations. The mechanisms we give have approximation ratios close to the best possible for both on-line and off-line scenarios. This is the first result where non-VCG mechanisms are derived for non-single minded bidders for a natural model of combinatorial auctions.

We study the role that privacy-preserving algorithms, which prevent the leakage of specific information about participants, can play in the design of mechanisms for strategic agents, which must encourage players to honestly report information. Specifically, we show that the recent notion of differential privacy [15, 14], in addition to its own intrinsic virtue, can ensure that participants have limited effect on the outcome of the mechanism, and as a consequence have limited incentive to lie. More precisely, mechanisms with differential privacy are approximate dominant strategy under arbitrary player utility functions, are automatically resilient to coalitions, and easily allow repeatability. We study several special cases of the unlimited supply auction problem, providing new results for digital goods auctions, attribute auctions, and auctions with arbitrary structural constraints on the prices. As an important prelude to developing a privacy-preserving auction mechanism, we introduce and study a generalization of previous privacy work that accommodates the high sensitivity of the auction setting, where a single participant may dramatically alter the optimal fixed price, and a slight change in the offered price may take the revenue from optimal to zero. 1

This paper deals with the design of efficiently computable incentive compatible, or truthful, mechanisms for combinatorial optimization problems with multi-parameter agents. We focus on approximation algorithms for NP-hard mechanism design problems. These algorithms need to satisfy certain monotonicity properties to ensure truthfulness. Since most of the known approximation techniques do not fulfill these properties, we study alternative techniques. Our first contribution is a quite general method to transform a pseudopolynomial algorithm into a monotone FPTAS. This can be applied to various problems like, e.g., knapsack, constrained shortest path, or job scheduling with deadlines. For example, the monotone FPTAS for the knapsack problem gives a very efficient, truthful mechanism for single-minded multi-unit auctions. The best previous result for such auctions was a 2-approximation. In addition,

We consider a game theoretic knapsack problem that has application to auctions for selling advertisements on Internet search engines. Consider n agents each wishing to place an object in the knapsack. Each agent has a private valuation for having their object in the knapsack and each object has a publicly known size. For this setting, we consider the design of auctions in which agents have an incentive to truthfully reveal their private valuations. Following the framework of Goldberg et al. [10], we look to design an auction that obtains a constant fraction of the profit obtainable by a natural optimal pricing algorithm that knows the agents ’ valuations and object sizes. We give an auction that obtains a constant factor approximation in the non-trivial special case where the knapsack has unlimited capacity. We then reduce the limited capacity version of the problem to the unlimited capacity version via an approximately efficient auction (i.e., one that maximizes the social welfare). This reduction follows from generalizable principles. 1

Abstract We prove semi-logarithmic inapproximability for a maximization problem called unique coverage:given a collection of sets, find a subcollection that maximizes the number of elements covered exactly once. Specifically, assuming that NP 6 ` BPTIME(2n " ) for an arbitrary "> 0, we prove O(1 / logoe n) inapproximability for some constant oe = oe("). We also prove O(1 / log1/3- " n) inapproximability, forany "> 0, assuming that refuting random instances of 3SAT is hard on average; and prove O(1 / log n)inapproximability under a plausible hypothesis concerning the hardness of another problem, balanced bipartite independent set. We establish an \Omega (1 / log n)-approximation algorithm, even for a moregeneral (budgeted) setting, and obtain an \Omega (1 / log B)-approximation algorithm when every set hasat most B elements. We also show that our inapproximability results extend to envy-free pricing, animportant problem in computational economics. We describe how the (budgeted) unique coverage problem, motivated by real-world applications, has close connections to other theoretical problemsincluding max cut, maximum coverage, and radio broadcasting. 1 Introduction In this paper we consider the approximability of the following natural maximization analog of set cover: Unique Coverage Problem. Given a universe U = {e1,..., en} of elements, and given a collection S = {S1,..., Sm} of subsets of U. Find a subcollection S0 ` S to maximize the number of elements that are uniquely covered, i.e., appear in exactly one set of S 0.

This paper introduces a new distinctive class of combinatorial auction protocols called priceoriented, rationing-free (PORF) protocols. The outline of a PORF protocol is as follows: (i) for each bidder, the price of each bundle of goods is determined independently of his/her own declaration (while it can depend on the declarations of other bidders), (ii) we allocate each bidder a bundle that maximizes his/her utility independently of the allocations of other bidders (i.e., rationing-free). Although a PORF protocol appears quite different from traditional protocol descriptions, surprisingly, it is a sufficient and necessary condition for a protocol to be strategy-proof. Furthermore, we show that a PORF protocol satisfying additional conditions is false-name-proof; at the same time, any falsename-proof protocol can be described as a PORF protocol that satisfies the additional conditions. A PORF protocol is an innovative characterization of strategy-proof protocols and the first attempt to characterize false-name-proof protocols. Such a characterization is not only theoretically significant but also useful in practice, since it can serve as a guideline for developing new strategy/false-name proof protocols. We present a new false-nameproof protocol based on the concept of a PORF protocol. 1

The widespread deployment of high-speed internet access is ushering in a new era of distributed computing, in which parties both contribute to a global pool of shared resources and access the pooled resources to support their own computing needs. We argue that system designers must explicitly address the self-interest of individual parties if these next-generation computing systems are to flourish. We propose strcteg37;roo f computirg, a vision for an open computing infrastructure in which resouree allocation and negotiation schemes are incentive-compatible, and individual parties can treat other resources as their own. In this paper we outline key guiding principles for the vision of strategyproof computing, define the strategyproof computing paradigm, and lay out a systems-related research agenda.

Abstract. In a combinatorial auction k different items are sold to n bidders, where the objective of the seller is to maximize the revenue. The main difficulty to find an optimal allocation is due to the fact that the valuation function of each bidder for bundles of items is not necessarily an additive function over the items. An auction with budget constraints is a common special case where bidders generally have additive valuations, yet they have a limit on their maximal valuation. Auctions with budget constraints were analyzed by Lehmann, Lehmann and Nisan [11], as part of a wider class of auctions, where they have shown that maximizing the revenue is NP-hard, and presented a greedy 2-approximation algorithm. In this paper we present exact and approximate algorithms for auctions with budget constraints. We present a randomized algorithm with an e approximation ratio of ≈ 1.582, which can be derandomized. We e−1 analyze the special case where all bidders have the same budget constraint, and show an algorithm whose approximation ratio is between 1.3837 and 1.3951. We also present an FPTAS for the case of a constant number of bidders. 1