We study a class of single round, sealed bid auctions for items in unlimited supply such as digital goods. We focus on auctions that are truthful and competitive. Truthful auctions encourage bidders to bid their utility; competitive auctions yield revenue within a constant factor of the revenue for optimal fixed pricing. We show that for any truthful auction, even a multi-price auction, the expected revenue does not exceed that for optimal fixed pricing. We also give a bound on how far the revenue for optimal fixed pricing can be from the total market utility. We show that several randomized auctions are truthful and competitive under certain assumptions, and that no truthful deterministic auction is competitive. We present simulation results which confirm that our auctions compare favorably to fixed pricing. Some of our results extend to bounded supply markets, for which we also get truthful and competitive auctions.

We give a general technique to obtain approximation mechanisms that are truthful in expectation.We show that for packing domains, any ff-approximation algorithm that also bounds the integrality gapof the LP relaxation of the problem by ff can be used to construct an ff-approximation mechanismthat is truthful in expectation. This immediately yields a variety of new and significantly improved results for various problem domains and furthermore, yields truthful (in expectation) mechanisms withguarantees that match the best known approximation guarantees when truthfulness is not required. In particular, we obtain the first truthful mechanisms with approximation guarantees for a variety of multi-parameter domains. We obtain truthful (in expectation) mechanisms achieving approximation guarantees of O( p m) for combinatorial auctions (CAs), (1 + ffl) for multi-unit CAs with B = \Omega (log m) copies ofeach item, and 2 for multi-parameter knapsack problems (multi-unit auctions). Our construction is based on considering an LP relaxation of the problem and using the classicVCG [25, 9, 12] mechanism to obtain a truthful mechanism in this fractional domain. We argue that the (fractional) optimal solution scaled down by ff, where ff is the integrality gap of the problem, canbe represented as a convex combination of integer solutions, and by viewing this convex combination as specifying a probability distribution over integer solutions, we get a randomized, truthful in expectationmechanism. Our construction can be seen as a way of exploiting VCG in a computational tractable way even when the underlying social-welfare maximization problem is NP-hard.

We show that any communication finding a Pareto efficient allocation in a private-information economy must also discover supporting Lindahl prices. In particular, efficient allocation of L indivisible objects requires naming a price for each of the 2 L ¡1 bundles. Furthermore, exponential communication in L is needed just to ensure a higher share of surplus than that realized by auctioning all items as a bundle, or even a higher expected surplus (for some probability distribution over valuations). When the valuations are submodular, efficiency still requires exponential communication (and fully polynomial approximation is impossible). When the objects are homogeneous, arbitrarily good approximation is obtained using exponentially less communication than that needed for exact efficiency.

We study the problem of pricing items for sale to consumers so as to maximize the seller’s revenue. We assume that for each consumer, we know the maximum amount he would be willing to pay for each bundle of items, and want to find pricings of the items with corresponding allocations that maximize seller profit and at the same time are envy-free, which is a natural fairness criterion requiring that consumers are maximally happy with the outcome they receive given the pricing. We study this problem for two important classes of inputs: unit demand consumers, who want to buy at most one item from among a selection they are interested in, and single-minded consumers, who want to buy one particular subset, but only if they can afford it. We show that computing envy-free prices to maximize the seller’s revenue is APX-hard in both of these cases, and give a logarithmic approximation algorithm for them. For several interesting special cases, we derive polynomial-time algorithms. Furthermore, we investigate some connections with the corresponding mechanism design problem, in which the consumer’s preferences are private values: for this case, we give a log-competitive truthful mechanism.

Abstract not found

We design two computationally-efficient incentive-compatible mechanisms for combinatorial auctions with general bidder preferences. Both mechanisms are randomized, and are incentive-compatible in the universal sense. This is in contrast to recent previous work that only addresses the weaker notion of incentive compatibility in expectation. The first mechanism obtains an O(pm)-approximation of the optimal social welfare for arbitrary bidder valuations -- this is the best approximation possible in polynomial time. The second one obtains an O(log2 m)- approximation for a subclass of bidder valuations that includes all submodular bidders. This improves over the best previously obtained incentive-compatible mechanism for this class which only provides an O(pm)-approximation.

Market-driven dynamic spectrum auctions can drastically improve the spectrum availability for wireless networks struggling to obtain additional spectrum. However, they face significant challenges due to the fear of market manipulation. A truthful or strategy-proof spectrum auction eliminates the fear by enforcing players to bid their true valuations of the spectrum. Hence bidders can avoid the expensive overhead of strategizing over others and the auctioneer can maximize its revenue by assigning spectrum to bidders who value it the most. Conventional truthful designs, however, either fail or become computationally intractable when applied to spectrum auctions. In this paper, we propose VERITAS, a truthful and computationally-efficient spectrum auction to support an eBay-like dynamic spectrum market. VERITAS makes an important contribution of maintaining truthfulness while maximizing spectrum utilization. We show analytically that VERITAS is truthful, efficient, and has a polynomial complexity of O(n 3 k) when n bidders compete for k spectrum bands. Simulation results show that VERITAS outperforms the extensions of conventional truthful designs by up to 200 % in spectrum utilization. Finally, VERITAS supports diverse bidding formats and enables the auctioneer to reconfigure allocations for multiple market objectives.

We solve a shortest path problem that is motivated by recent interest in pricing networks or other computational resources. Informally, how much is an edge in a network worth to a user who wants to send data between two nodes along a shortest path? If the network is a decentralized entity, such as the Internet, in which multiple self-interested agents own different parts of the network, then auctionbased pricing seems appropriate. A celebrated result from auction theory shows that the use of Vickrey pricing motivates the owners of the network resources to bid truthfully. In Vickrey's scheme, each agent is compensated in proportion to the marginal utility he brings to the auction. In the context of shortest path routing, an edge's utility is the value by which it lowers the length of the shortest path---the difference between the shortest path lengths with and without the edge. Our problem is to compute these marginal values for all the edges of the network efficiently. The na ve method requires solving the single-source shortest path problem up to n times, for an n-node network. We show that the Vickrey prices for all the edges can be computed in the same asymptotic time complexity as one single-source shortest path problem. This solves an open problem posed by Nisan and Ronen [12]. 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 present a monotone PTAS for the generalized assignment problem with any bounded number of parameters per agent. The most efficient way to solve packing integer programs (PIPs) is LP-based randomized rounding, which also is in general not monotone. We show that primal-dual greedy algorithms achieve almost the same approximation ratios for PIPs as randomized rounding. The advantage is that these algorithms are inherently monotone. This way, we can significantly improve the approximation ratios of truthful mechanisms for various fundamental mechanism design problems like single-minded combinatorial auctions (CAs), unsplittable flow routing and multicast routing. Our approximation algorithms can also be used for the winner determination in CAs with general bidders specifying their bids through an oracle.

Spectrum is a critical yet scarce resource and it has been shown that dynamic spectrum access can significantly improve spectrum utilization. To achieve this, it is important to incentivize the primary license holders to open up their under-utilized spectrum for sharing. In this paper we present a secondary spectrum market where a primary license holder can sell access to its unused or under-used spectrum resources in the form of certain fine-grained spectrumspace-time unit. Secondary wireless service providers can purchase such contracts to deploy new service, enhance their existing service, or deploy ad hoc service to meet flash crowds demand. Within the context of this market, we investigate how to use auction mechanisms to allocate and price spectrum resources so that the primary license holder’s revenue is maximized. We begin by classifying a number of alternative auction formats in terms of spectrum demand. We then study a specific auction format where secondary wireless service providers have demands for fixed locations (cells). We propose an optimal auction based on the concept of virtual valuation. Assuming the knowledge of valuation distributions, the optimal auction uses the Vickrey-Clarke-Groves (VCG) mechanism to maximize the expected revenue while enforcing truthfulness. To reduce the computational complexity, we further design a truthful suboptimal auction with polynomial time complexity. It uses a monotone allocation and critical value payment to enforce truthfulness. Simulation results show that this suboptimal auction can generate stable expected revenue.