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Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords
 American Economic Review
, 2005
"... We investigate the “generalized secondprice ” (GSP) auction, a new mechanism used by search engines to sell online advertising. Although GSP looks similar to the VickreyClarkeGroves (VCG) mechanism, its properties are very different. Unlike the VCG mechanism, GSP generally does not have an equili ..."
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Cited by 342 (16 self)
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We investigate the “generalized secondprice ” (GSP) auction, a new mechanism used by search engines to sell online advertising. Although GSP looks similar to the VickreyClarkeGroves (VCG) mechanism, its properties are very different. Unlike the VCG mechanism, GSP generally does not have an equilibrium in dominant strategies, and truthtelling is not an equilibrium of GSP. To analyze the properties of GSP, we describe the generalized English auction that corresponds to GSP and show that it has a unique equilibrium. This is an ex post equilibrium, with the same payoffs to all players as the dominant strategy equilibrium of VCG. (JEL D44, L81, M37) This paper investigates a new auction mechanism, which we call the “generalized secondprice” auction, or GSP. GSP is tailored to the unique environment of the market for online ads, and neither the environment nor the mechanism has previously been studied in the mechanism design literature. While studying the properties of a novel mechanism is often fascinating in itself, our interest is also motivated by the spectacular commercial success of GSP. It is the dominant transaction mechanism in a large and rapidly growing industry. For example, Google’s total revenue in 2005 was $6.14 billion. Over 98 percent of its revenue came from GSP auctions. Yahoo!’s total revenue in 2005 was $5.26 billion. A large share of Yahoo!’s revenue is derived from sales via GSP auctions. It is believed that over half of Yahoo!’s revenue is derived from sales via GSP auctions. As of May 2006, the combined market capitalization of these companies exceeded $150 billion. Let us briefly describe how these auctions work. When an Internet user enters a search
Taming the computational complexity of combinatorial auctions: Optimal and approximate approaches
, 1999
"... In combinatorial auctions, multiple goods are sold simultaneously and bidders may bid for arbitrary combinations of goods. Determining the outcome of such an auction is an optimization problem that is NPcomplete in the general case. We propose two methods of overcoming this apparent intractability. ..."
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Cited by 267 (9 self)
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In combinatorial auctions, multiple goods are sold simultaneously and bidders may bid for arbitrary combinations of goods. Determining the outcome of such an auction is an optimization problem that is NPcomplete in the general case. We propose two methods of overcoming this apparent intractability. The first method, which is guaranteed to be optimal, reduces running time by structuring the search space so that a modified depthfirst search usually avoids even considering allocations that contain conflicting bids. Caching and pruning are also used to speed searching. Our second method is a heuristic, marketbased approach. It sets up a virtual multiround auction in which a virtual agent represents each original bid bundle and places bids, according to a fixed strategy, for each good in that bundle. We show through experiments on synthetic data that (a) our first method finds optimal allocations quickly and offers good anytime performance, and (b) in many cases our second method, despite lacking guarantees regarding optimality or running time, quickly reaches solutions that are nearly optimal. 1 Combinatorial Auctions Auction theory has received increasing attention from computer scientists in recent years. 1 One reason is the explosion of internetbased auctions. The use of auctions in businesstobusiness trades is also increasing rapidly [Cortese and Stepanek, 1998]. Within AI there is growing interest in using auction mechanisms to solve distributed resource allocation problems. For example, auctions and other market mechanisms are used in network bandwidth allocation, distributed configuration design, factory scheduling, and operating system memory allocation [Clearwater, 1996]. Marketoriented programming has
Bidding and Allocation in Combinatorial Auctions
 In ACM Conference on Electronic Commerce
, 2000
"... When an auction of multiple items is performed, it is often desirable to allow bids on combinations of items, as opposed to only on single items. Such an auction is often called "combinatorial ", and the exponential number of possible combinations results in computational intractability of many a ..."
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Cited by 242 (11 self)
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When an auction of multiple items is performed, it is often desirable to allow bids on combinations of items, as opposed to only on single items. Such an auction is often called "combinatorial ", and the exponential number of possible combinations results in computational intractability of many aspects regarding such an auction. This paper considers two of these aspects: the bidding language and the allocation algorithm. First we consider which kinds of bids on combinations are allowed and how, i.e. in what language, they are specified. The basic tradeoff is the expressibility of the language versus its simplicity. We consider and formalize several bidding languages and compare their strengths. We prove exponential separations between the expressive power of different languages, and show that one language, "ORbids with phantom items", can polynomially simulate the others. We then consider the problem of determining the best allocation  a problem known to be computationally intractable. We suggest an approach based on Linear Programming (LP) and motivate it. We prove that the LP approach finds an optimal allocation if and only if prices can be attached to single items in the auction. We pinpoint several classes of auctions where this is the case, and suggest greedy and branchandbound heuristics based on LP for other cases. 1
A BGPbased Mechanism for LowestCost Routing
, 2002
"... The routing of traffic between... this paper, we address the problem of interdomain routing from a mechanismdesign point of view. The application of mechanismdesign principles to the study of routing is the subject of earlier work by Nisan and Ronen [15] and Hershberger and Suri [11]. In this pape ..."
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Cited by 230 (17 self)
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The routing of traffic between... this paper, we address the problem of interdomain routing from a mechanismdesign point of view. The application of mechanismdesign principles to the study of routing is the subject of earlier work by Nisan and Ronen [15] and Hershberger and Suri [11]. In this paper, we formulate and solve a version of the routingmechanism design problem that is different from the previously studied version in three ways that make it more accurately reflective of realworld interdomain routing: (1) we treat the nodes as strategic agents, rather than the links; (2) our mechanism computes lowestcost routes for all sourcedestination pairs and payments for transit nodes on all of the routes (rather than computing routes and payments for only one sourcedestination pair at a time, as is done in [15,11]); (3) we show how to compute our mechanism with a distributed algorithm that is a straightforward extension to BGP and causes only modest increases in routingtable size and convergence time (in contrast with the centralized algorithms used in [15,11]). This approach of using an existing protocol as a substrate for distributed computation may prove useful in future development of Internet algorithms generally, not only for routing or pricing problems. Our design and analysis of a strategyproof, BGPbased routing mechanism provides a new, promising direction in distributed algorithmic mechanism design, which has heretofore been focused mainly on multicast cost sharing.
Coalition Structure Generation with Worst Case Guarantees
, 1999
"... Coalition formation is a key topic in multiagent systems. One may prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. Furthermore, finding the optimal coalition ..."
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Cited by 209 (10 self)
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Coalition formation is a key topic in multiagent systems. One may prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. Furthermore, finding the optimal coalition structure is NPcomplete. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum? We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algorithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also significantly outperforms its obvious contenders. Finally, we show how to distribute the desired
Efficient power control via pricing in wireless data networks
 IEEE Transactions on Communication
, 2000
"... A major challenge in operation of wireless communications systems is the efficient use of radio resources. One important component of radio resource management is power control, which has been studied extensively in the context of voice communications. With increasing demand for wireless data servic ..."
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Cited by 201 (6 self)
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A major challenge in operation of wireless communications systems is the efficient use of radio resources. One important component of radio resource management is power control, which has been studied extensively in the context of voice communications. With increasing demand for wireless data services, it is necessary to establish power control algorithms for information sources other than voice. We present a power control solution for wireless data in the analytical setting of a game theoretic framework. In this context, the quality of service (QoS) a wireless terminal receives is referred to as the utility and distributed power control is a noncooperative power control game where users maximize their utility. The outcome of the game results in a Nash equilibrium that is ine#cient. We introduce pricing of transmit powers in order to obtain Pareto improvement of the noncooperative power control game, i.e. to obtain improvements in user utilities relative to the case with no pricing. Specifically, we consider a pricing function that is a linear function of the transmit power. The simplicity of the pricing function allows a distributed implementation where the price can be broadcast by the base station to all the terminals. We see that pricing is especially helpful in a heavily loaded system.
Truthful Mechanisms for OneParameter Agents
"... In this paper, we show how to design truthful (dominant strategy) mechanisms for several combinatorial problems where each agent’s secret data is naturally expressed by a single positive real number. The goal of the mechanisms we consider is to allocate loads placed on the agents, and an agent’s sec ..."
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Cited by 191 (4 self)
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In this paper, we show how to design truthful (dominant strategy) mechanisms for several combinatorial problems where each agent’s secret data is naturally expressed by a single positive real number. The goal of the mechanisms we consider is to allocate loads placed on the agents, and an agent’s secret data is the cost she incurs per unit load. We give an exact characterization for the algorithms that can be used to design truthful mechanisms for such load balancing problems using appropriate side payments. We use our characterization to design polynomial time truthful mechanisms for several problems in combinatorial optimization to which the celebrated VCG mechanism does not apply. For scheduling related parallel machines (QjjCmax), we give a 3approximation mechanism based on randomized rounding of the optimal fractional solution. This problem is NPcomplete, and the standard approximation algorithms (greedy loadbalancing or the PTAS) cannot be used in truthful mechanisms. We show our mechanism to be frugal, in that the total payment needed is only a logarithmic factor more than the actual costs incurred by the machines, unless one machine dominates the total processing power. We also give truthful mechanisms for maximum flow, Qjj P Cj (scheduling related machines to minimize the sum of completion times), optimizing an affine function over a fixed set, and special cases of uncapacitated facility location. In addition, for Qjj P wjCj (minimizing the weighted sum of completion times), we prove a lower bound of 2 p 3 for the best approximation ratio achievable by a truthful mechanism.
Computationally feasible VCG mechanisms
 In Proceedings of the Second ACM Conference on Electronic Commerce (EC’00
, 2000
"... A major achievement of mechanism design theory is a general method for the construction of truthful mechanisms called VCG. When applying this method to complex problems such as combinatorial auctions, a difficulty arises: VCG mechanisms are required to compute optimal outcomes and are therefore comp ..."
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Cited by 188 (5 self)
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A major achievement of mechanism design theory is a general method for the construction of truthful mechanisms called VCG. When applying this method to complex problems such as combinatorial auctions, a difficulty arises: VCG mechanisms are required to compute optimal outcomes and are therefore computationally infeasible. However, if the optimal outcome is replaced by the results of a suboptimal algorithm, the resulting mechanism (termed VCGbased) is no longer necessarily truthful. The first part of this paper studies this phenomenon in depth and shows that it is near universal. Specifically, we prove that essentially all reasonable approximations or heuristics for combinatorial auctions as well as a wide class of cost minimization problems yield nontruthful VCGbased mechanisms. We generalize these results for affine maximizers. The second part of this paper proposes a general method for circumventing the above problem. We introduce a modification of VCGbased mechanisms in which the agents are given a chance to improve the output of the underlying algorithm. When the agents behave truthfully, the welfare obtained by the mechanism is at least as good as the one obtained by the algorithm’s output. We provide a strong rationale for truthtelling behavior. Our method satisfies individual rationality as well.
Truth revelation in approximately efficient combinatorial auctions
 Journal of the ACM
, 2002
"... 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 ..."
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Cited by 182 (1 self)
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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.
Distributed Rational Decision Making
, 1999
"... Introduction Automated negotiation systems with selfinterested agents are becoming increasingly important. One reason for this is the technology push of a growing standardized communication infrastructureInternet, WWW, NII, EDI, KQML, FIPA, Concordia, Voyager, Odyssey, Telescript, Java, etco ..."
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Cited by 167 (0 self)
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Introduction Automated negotiation systems with selfinterested agents are becoming increasingly important. One reason for this is the technology push of a growing standardized communication infrastructureInternet, WWW, NII, EDI, KQML, FIPA, Concordia, Voyager, Odyssey, Telescript, Java, etcover which separately designed agents belonging to different organizations can interact in an open environment in realtime and safely carry out transactions. The second reason is strong application pull for computer support for negotiation at the operative decision making level. For example, we are witnessing the advent of small transaction electronic commerce on the Internet for purchasing goods, information, and communication bandwidth [29]. There is also an industrial trend toward virtual enterprises: dynamic alliances of small, agile enterprises which together can take advantage of economies of scale when available (e.g., respond to mor