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200
Sharing the Cost of Multicast Transmissions
, 2001
"... We investigate costsharing algorithms for multicast transmission. Economic considerations point to two distinct mechanisms, marginal cost and Shapley value, as the two solutions most appropriate in this context. We prove that the former has a natural algorithm that uses only two messages per link o ..."
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Cited by 291 (19 self)
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We investigate costsharing algorithms for multicast transmission. Economic considerations point to two distinct mechanisms, marginal cost and Shapley value, as the two solutions most appropriate in this context. We prove that the former has a natural algorithm that uses only two messages per link of the multicast tree, while we give evidence that the latter requires a quadratic total number of messages. We also show that the welfare value achieved by an optimal multicast tree is NPhard to approximate within any constant factor, even for boundeddegree networks. The lowerbound proof for the Shapley value uses a novel algebraic technique for bounding from below the number of messages exchanged in a distributed computation; this technique may prove useful in other contexts as well.
Distributed Algorithmic Mechanism Design: Recent Results and Future Directions
, 2002
"... Distributed Algorithmic Mechanism Design (DAMD) combines theoretical computer science’s traditional focus on computational tractability with its more recent interest in incentive compatibility and distributed computing. The Internet’s decentralized nature, in which distributed computation and autono ..."
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Cited by 288 (22 self)
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Distributed Algorithmic Mechanism Design (DAMD) combines theoretical computer science’s traditional focus on computational tractability with its more recent interest in incentive compatibility and distributed computing. The Internet’s decentralized nature, in which distributed computation and autonomous agents prevail, makes DAMD a very natural approach for many Internet problems. This paper first outlines the basics of DAMD and then reviews previous DAMD results on multicast cost sharing and interdomain routing. The remainder of the paper describes several promising research directions and poses some specific open problems.
The price of stability for network design with fair cost allocation
 In Proceedings of the 45th Annual Symposium on Foundations of Computer Science (FOCS
, 2004
"... Abstract. Network design is a fundamental problem for which it is important to understand the effects of strategic behavior. Given a collection of selfinterested agents who want to form a network connecting certain endpoints, the set of stable solutions — the Nash equilibria — may look quite differ ..."
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Cited by 279 (27 self)
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Abstract. Network design is a fundamental problem for which it is important to understand the effects of strategic behavior. Given a collection of selfinterested agents who want to form a network connecting certain endpoints, the set of stable solutions — the Nash equilibria — may look quite different from the centrally enforced optimum. We study the quality of the best Nash equilibrium, and refer to the ratio of its cost to the optimum network cost as the price of stability. The best Nash equilibrium solution has a natural meaning of stability in this context — it is the optimal solution that can be proposed from which no user will defect. We consider the price of stability for network design with respect to one of the most widelystudied protocols for network cost allocation, in which the cost of each edge is divided equally between users whose connections make use of it; this fairdivision scheme can be derived from the Shapley value, and has a number of basic economic motivations. We show that the price of stability for network design with respect to this fair cost allocation is O(log k), where k is the number of users, and that a good Nash equilibrium can be achieved via bestresponse dynamics in which users iteratively defect from a starting solution. This establishes that the fair cost allocation protocol is in fact a useful mechanism for inducing strategic behavior to form nearoptimal equilibria. We discuss connections to the class of potential games defined by Monderer and Shapley, and extend our results to cases in which users are seeking to balance network design costs with latencies in the constructed network, with stronger results when the network has only delays and no construction costs. We also present bounds on the convergence time of bestresponse dynamics, and discuss extensions to a weighted game.
Approximation algorithms for combinatorial auctions with complementfree bidders
 In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (STOC
, 2005
"... We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items m and in the number of bidders n, even though the “input size ” is exponential in m. The first algori ..."
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Cited by 137 (27 self)
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We exhibit three approximation algorithms for the allocation problem in combinatorial auctions with complement free bidders. The running time of these algorithms is polynomial in the number of items m and in the number of bidders n, even though the “input size ” is exponential in m. The first algorithm provides an O(log m) approximation. The second algorithm provides an O ( √ m) approximation in the weaker model of value oracles. This algorithm is also incentive compatible. The third algorithm provides an improved 2approximation for the more restricted case of “XOS bidders”, a class which strictly contains submodular bidders. We also prove lower bounds on the possible approximations achievable for these classes of bidders. These bounds are not tight and we leave the gaps as open problems. 1
Applications of Approximation Algorithms to Cooperative Games
 STOC'01
, 2001
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Competitive Auctions
"... We study a class of singleround, sealedbid auctions for an item in unlimited supply, such as adigital good. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages bidders to bid their true valuations) and on all inputs yields profit that is withina co ..."
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Cited by 114 (12 self)
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We study a class of singleround, sealedbid auctions for an item in unlimited supply, such as adigital good. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages bidders to bid their true valuations) and on all inputs yields profit that is withina constant factor of the profit of the optimal single sale price. We justify the use of optimal single price profit as a benchmark for evaluating a competitive auctions profit. We exhibitseveral randomized competitive auctions and show that there is no symmetric deterministic competitive auction. Our results extend to bounded supply markets, for which we also givecompetitive auctions.
Boosted sampling: Approximation algorithms for stochastic optimization problems
 IN: 36TH STOC
, 2004
"... Several combinatorial optimization problems choose elements to minimize the total cost of constructing a feasible solution that satisfies requirements of clients. In the STEINER TREE problem, for example, edges must be chosen to connect terminals (clients); in VERTEX COVER, vertices must be chosen t ..."
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Cited by 99 (25 self)
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Several combinatorial optimization problems choose elements to minimize the total cost of constructing a feasible solution that satisfies requirements of clients. In the STEINER TREE problem, for example, edges must be chosen to connect terminals (clients); in VERTEX COVER, vertices must be chosen to cover edges (clients); in FACILITY LOCATION, facilities must be chosen and demand vertices (clients) connected to these chosen facilities. We consider a stochastic version of such a problem where the solution is constructed in two stages: Before the actual requirements materialize, we can choose elements in a first stage. The actual requirements are then revealed, drawn from a prespecified probability distribution π; thereupon, some more elements may be chosen to obtain a feasible solution for the actual requirements. However, in this second (recourse) stage, choosing an element is costlier by a factor of σ> 1. The goal is to minimize the first stage cost plus the expected second stage cost. We give a general yet simple technique to adapt approximation algorithms for several deterministic problems to their stochastic versions via the following method. • First stage: Draw σ independent sets of clients from the distribution π and apply the approximation algorithm to construct a feasible solution for the union of these sets. • Second stage: Since the actual requirements have now been revealed, augment the firststage solution to be feasible for these requirements.
Competitive Generalized Auctions
, 2002
"... We describe mechanisms for auctions that are simultaneously truthful (alternately known as strategyproof or incentivecompatible) and guarantee high "net" profit. We make use of appropriate variants of competitive analysis of algorithms in designing and analyzing our mechanisms. Thus, we ..."
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Cited by 97 (20 self)
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We describe mechanisms for auctions that are simultaneously truthful (alternately known as strategyproof or incentivecompatible) and guarantee high "net" profit. We make use of appropriate variants of competitive analysis of algorithms in designing and analyzing our mechanisms. Thus, we do not require any probabilistic assumptions on bids. We present
Knapsack auctions
"... 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 pu ..."
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Cited by 77 (12 self)
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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 nontrivial 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.
Strong price of anarchy
 In SODA
, 2007
"... A strong equilibrium (Aumann 1959) is a pure Nash equilibrium which is resilient to deviations by coalitions. We define the strong price of anarchy to be the ratio of the worst case strong equilibrium to the social optimum. In contrast to the traditional price of anarchy, which quantifies the loss i ..."
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Cited by 76 (11 self)
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A strong equilibrium (Aumann 1959) is a pure Nash equilibrium which is resilient to deviations by coalitions. We define the strong price of anarchy to be the ratio of the worst case strong equilibrium to the social optimum. In contrast to the traditional price of anarchy, which quantifies the loss incurred due to both selfishness and lack of coordination, the strong price of anarchy isolates the loss originated from selfishness from that obtained due to lack of coordination. We study the strong price of anarchy in two settings, one of job scheduling and the other of network creation. In the job scheduling game we show that for unrelated machines the strong price of anarchy can be bounded as a function of the number of machines and the size of the coalition. For the network creation game we show that the strong price of anarchy is at most 2. In both cases we show that a strong equilibrium always exists, except for a well defined subset of network creation games. ∗ This work was supported in part by the IST Programme of the European Community, under the PASCAL