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113
Multi-unit auctions with budget-constrained bidders
- In Proceedings of the 7th ACM Conference on Electronic Commerce
, 2005
"... We study a multi-unit auction with multiple bidders, each of whom has a private valuation and a budget. The truthful mechanisms of such an auction are characterized, in the sense that, under standard assumptions, we prove that it is impossible to design a non-trivial truthful auction which allocates ..."
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Cited by 92 (10 self)
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We study a multi-unit auction with multiple bidders, each of whom has a private valuation and a budget. The truthful mechanisms of such an auction are characterized, in the sense that, under standard assumptions, we prove that it is impossible to design a non-trivial truthful auction which allocates all units, while we provide the design of an asymptotically revenue-maximizing truthful mechanism which may allocate only some of the units. Our asymptotic parameter is a budget dominance parameter which measures the size of the budget of a single agent relative to the maximum revenue. We discuss the relevance of these results for the design of Internet ad auctions.
Approximation algorithms and online mechanisms for item pricing
, 2007
"... We present approximation and online algorithms for problems of pricing a collection of items for sale so as to maximize the seller’s revenue in an unlimited supply setting. Our first result is an O(k)-approximation algorithm for pricing items to single-minded bidders who each want at most k items. ..."
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Cited by 76 (9 self)
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We present approximation and online algorithms for problems of pricing a collection of items for sale so as to maximize the seller’s revenue in an unlimited supply setting. Our first result is an O(k)-approximation algorithm for pricing items to single-minded bidders who each want at most k items. This improves over work of Briest and Krysta (2006) who achieve an O(k2) bound. For the case k = 2, where we obtain a 4-approximation, this can be viewed as the following graph vertex pricing problem: given a (multi) graph G with valuations wi j on the edges, find prices pi ≥ 0 for the vertices to maximize {(i, j):wi j≥pi+p j} (pi + p j). We also improve the approximation of Guruswami et al. (2005) for the “highway problem” in which all desired subsets are intervals on a line, from O(logm+ logn) to O(logn), where m is the number of bidders and n is the number of items. Our approximation algorithms can
Simple versus Optimal Mechanisms
"... The monopolist’s theory of optimal single-item auctions for agents with independent private values can be summarized by two statements. The first is from Myerson [8]: the optimal auction is Vickrey with a reserve price. The second is from Bulow and Klemperer [1]: it is better to recruit one more bid ..."
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Cited by 76 (25 self)
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The monopolist’s theory of optimal single-item auctions for agents with independent private values can be summarized by two statements. The first is from Myerson [8]: the optimal auction is Vickrey with a reserve price. The second is from Bulow and Klemperer [1]: it is better to recruit one more bidder and run the Vickrey auction than to run the optimal auction. These results hold for single-item auctions under the assumption that the agents ’ valuations are independently and identically drawn from a distribution that satisfies a natural (and prevalent) regularity condition. These fundamental guarantees for the Vickrey auction fail to hold in general single-parameter agent mechanism design problems. We give precise (and weak) conditions under which approximate analogs of these two results hold, thereby demonstrating that simple mechanisms remain almost optimal in quite general single-parameter agent settings.
Multi-unit auctions with budget limits. In
- In Proc. of the 49th Annual Symposium on Foundations of Computer Science (FOCS),
, 2008
"... Abstract We study multi-unit auctions where the bidders have a budget constraint, a situation very common in practice that has received relatively little attention in the auction theory literature. Our main result is an impossibility: there are no incentive-compatible auctions that always produce a ..."
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Cited by 62 (7 self)
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Abstract We study multi-unit auctions where the bidders have a budget constraint, a situation very common in practice that has received relatively little attention in the auction theory literature. Our main result is an impossibility: there are no incentive-compatible auctions that always produce a Pareto-optimal allocation. We also obtain some surprising positive results for certain special cases. JEL Classification Numbers: C70, D44, D82 Keywords: Multi-Unit Auctions, Budget Constraints, Pareto Optimality. * A preliminary version appeared in FOCS'08. We thank Peerapong Dhangwatnotai for pointing out an error in a previous version.
Worst-case optimal redistribution of VCG payments
- In Proceedings of the ACM Conference on Electronic Commerce (EC
, 2007
"... For allocation problems with one or more items, the wellknown Vickrey-Clarke-Groves (VCG) mechanism is efficient, strategy-proof, individually rational, and does not incur a deficit. However, the VCG mechanism is not (strongly) budget balanced: generally, the agents ’ payments will sum to more than ..."
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Cited by 58 (18 self)
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For allocation problems with one or more items, the wellknown Vickrey-Clarke-Groves (VCG) mechanism is efficient, strategy-proof, individually rational, and does not incur a deficit. However, the VCG mechanism is not (strongly) budget balanced: generally, the agents ’ payments will sum to more than 0. If there is an auctioneer who is selling the items, this may be desirable, because the surplus payment corresponds to revenue for the auctioneer. However, if the items do not have an owner and the agents are merely interested in allocating the items efficiently among themselves, any surplus payment is undesirable, because it will have to flow out of the system of agents. In 2006, Cavallo [3] proposed a mechanism that redistributes some of the VCG payment back to the agents, while maintaining efficiency, strategy-proofness, individual rationality, and the
Optimal mechanism design and money burning
- STOC ’08
, 2008
"... Mechanism design is now a standard tool in computer science for aligning the incentives of self-interested agents with the objectives of a system designer. There is, however, a fundamental disconnect between the traditional application domains of mechanism design (such as auctions) and those arising ..."
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Cited by 57 (15 self)
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Mechanism design is now a standard tool in computer science for aligning the incentives of self-interested agents with the objectives of a system designer. There is, however, a fundamental disconnect between the traditional application domains of mechanism design (such as auctions) and those arising in computer science (such as networks): while monetary transfers (i.e., payments) are essential for most of the known positive results in mechanism design, they are undesirable or even technologically infeasible in many computer systems. Classical impossibility results imply that the reach of mechanisms without transfers is severely limited. Computer systems typically do have the ability to reduce service quality—routing systems can drop or delay traffic, scheduling protocols can delay the release of jobs, and computational payment schemes can require computational payments from users (e.g., in spam-fighting systems). Service degradation is tantamount to requiring that users burn money, and such “payments ” can be used to influence the preferences of the agents at a cost of degrading the social surplus. We develop a framework for the design and analysis of money-burning mechanisms to maximize the residual surplus— the total value of the chosen outcome minus the payments required. Our primary contributions are the following. • We define a general template for prior-free optimal mechanism design that explicitly connects Bayesian optimal mechanism design, the dominant paradigm in economics, with worst-case analysis. In particular, we establish a general and principled way to identify appropriate performance benchmarks in prior-free mechanism design. • For general single-parameter agent settings, we char-
Robust game theory
, 2006
"... We present a distribution-free model of incomplete-information games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our “robust game” model relaxes the assumptions of Harsanyi’s Bayesian game model, and provides ..."
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Cited by 55 (0 self)
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We present a distribution-free model of incomplete-information games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our “robust game” model relaxes the assumptions of Harsanyi’s Bayesian game model, and provides an alternative distribution-free equilibrium concept, which we call “robust-optimization equilibrium, ” to that of the ex post equilibrium. We prove that the robust-optimization equilibria of an incomplete-information game subsume the ex post equilibria of the game and are, unlike the latter, guaranteed to exist when the game is finite and has bounded payoff uncertainty set. For arbitrary robust finite games with bounded polyhedral payoff uncertainty sets, we show that we can compute a robust-optimization equilibrium by methods analogous to those for identifying a Nash equilibrium of a finite game with complete information. In addition, we present computational results.
Approximation and Collusion in Multicast Cost Sharing
, 2004
"... in Proceedings of the 3rd ACM Conference on Electronic Commerce, Tampa FL, October 2001. This work was supported by the DoD University Research Initiative (URI) program administered by the Oce of Naval Research under Grant N00014-01-1-0795. ..."
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Cited by 52 (3 self)
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in Proceedings of the 3rd ACM Conference on Electronic Commerce, Tampa FL, October 2001. This work was supported by the DoD University Research Initiative (URI) program administered by the Oce of Naval Research under Grant N00014-01-1-0795.
Better redistribution with inefficient allocation in multi-unit auctions with unit demand
- In Proceedings of the ACM Conference on Electronic Commerce (EC
, 2008
"... For the problem of allocating one or more items among a group of competing agents, the Vickrey-Clarke-Groves (VCG) mechanism is strategy-proof and efficient. However, the VCG mechanism is not strongly budget balanced: in general, value flows out of the system of agents in the form of VCG payments, w ..."
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Cited by 29 (11 self)
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For the problem of allocating one or more items among a group of competing agents, the Vickrey-Clarke-Groves (VCG) mechanism is strategy-proof and efficient. However, the VCG mechanism is not strongly budget balanced: in general, value flows out of the system of agents in the form of VCG payments, which reduces the agents ’ utilities. In many settings, the objective is to maximize the sum of the agents’ utilities (taking payments into account). For this purpose, several VCG redistribution mechanisms have been proposed that redistribute a large fraction of the VCG payments back to the agents, in a way that maintains strategy-proofness and the non-deficit property. Unfortunately, sometimes even the best VCG redistribution mechanism fails to redistribute a substantial fraction of the VCG payments. This results in a low total utility for the agents, even though the items
Truthful and Competitive Double Auctions
, 2002
"... In this paper we consider the problem of designing a mechanism for double auctions where bidders each bid to buy or sell one unit of a single commodity. We assume that each bidder's utility value for the item is private to them and we focus on truthful mechanisms, ones were the bidders' op ..."
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Cited by 28 (8 self)
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In this paper we consider the problem of designing a mechanism for double auctions where bidders each bid to buy or sell one unit of a single commodity. We assume that each bidder's utility value for the item is private to them and we focus on truthful mechanisms, ones were the bidders' optimal strategy is to bid their true utility. The profit of the auctioneer is the difference between the total payments from buyers and total to the sellers. We aim to maximize this profit. We extend the competitive analysis framework of basic auctions [9] and give an upper bound on the profit of any truthful double auction. We then reduce the competitive double auction problem to basic auctions by showing that any competitive basic auction can be converted into a competitive double auction with a competitive ratio of twice that of the basic auction.
