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Matroids, Secretary Problems, and Online Mechanisms
"... We study a generalization of the classical secretary problem which we call the “matroid secretary problem”. In this problem, the elements of a matroid are presented to an online algorithm in random order. When an element arrives, the algorithm observes its value and must make an irrevocable decision ..."
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Cited by 36 (5 self)
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We study a generalization of the classical secretary problem which we call the “matroid secretary problem”. In this problem, the elements of a matroid are presented to an online algorithm in random order. When an element arrives, the algorithm observes its value and must make an irrevocable decision regarding whether or not to accept it. The accepted elements must form an independent set, and the objective is to maximize the combined value of these elements. This paper presents an O(log k)competitive algorithm for general matroids (where k is the rank of the matroid), and constantcompetitive algorithms for several special cases including graphic matroids, truncated partition matroids, and bounded degree transversal matroids. We leave as an open question the existence of constantcompetitive algorithms for general matroids. Our results have applications in welfaremaximizing online mechanism design for domains in which the sets of simultaneously satisfiable agents form a matroid.
An IroningBased Approach to Adaptive Online Mechanism Design in SingleValued Domains
 In Proceedings of the 22nd National Conference on Artificial Intelligence (AAAI’07), 94–101. Menlo Park
, 2007
"... Online mechanism design considers the problem of sequential decision making in a multiagent system with selfinterested agents. The agent population is dynamic and each agent has private information about its value for a sequence of decisions. We introduce a method (“ironing") to transform an ..."
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Cited by 29 (10 self)
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Online mechanism design considers the problem of sequential decision making in a multiagent system with selfinterested agents. The agent population is dynamic and each agent has private information about its value for a sequence of decisions. We introduce a method (“ironing") to transform an algorithm for online stochastic optimization into one that is incentivecompatible. Ironing achieves this by canceling decisions that violate a form of monotonicity. The approach is applied to the CONSENSUS algorithm and experimental results in a resource allocation domain show that not many decisions need to be canceled and that the overhead of ironing is manageable.
Singlevalue combinatorial auctions and algorithmic implementation in undominated strategies
 In ACM Symposium on Discrete Algorithms
, 2011
"... In this paper we are interested in general techniques for designing mechanisms that approximate the social welfare in the presence of selfish rational behavior. We demonstrate our results in the setting of Combinatorial Auctions (CA). Our first result is a general deterministic technique to decouple ..."
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Cited by 26 (2 self)
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In this paper we are interested in general techniques for designing mechanisms that approximate the social welfare in the presence of selfish rational behavior. We demonstrate our results in the setting of Combinatorial Auctions (CA). Our first result is a general deterministic technique to decouple the algorithmic allocation problem from the strategic aspects, by a procedure that converts any algorithm to a dominantstrategy ascending mechanism. This technique works for any single value domain, in which each agent has the same value for each desired outcome, and this value is the only private information. In particular, for “singlevalue CAs”, where each player desires any one of several different bundles but has the same value for each of them, our technique converts any approximation algorithm to a dominant strategy mechanism that almost preserves the original approximation ratio. Our second result provides the first computationally efficient deterministic mechanism for the case of singlevalue multiminded bidders (with private value and private desired bundles). The mechanism achieves an approximation to the social welfare which is close to the best possible in polynomial time (unless P=NP). This mechanism is an algorithmic implementation in undominated strategies, a notion that we define and justify, and is of independent interest. 1
Failures of the VCG Mechanism in Combinatorial Auctions and Exchanges
 IN INTERNATIONAL CONFERENCE ON AUTONOMOUS AGENTS AND MULTIAGENT SYSTEMS (AAMAS
, 2006
"... The VCG mechanism is the canonical method for motivating bidders in combinatorial auctions and exchanges to bid truthfully. We study two related problems concerning the VCG mechanism: the problem of revenue guarantees, and that of collusion. The existence of these problems even in oneitem settings ..."
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Cited by 20 (4 self)
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The VCG mechanism is the canonical method for motivating bidders in combinatorial auctions and exchanges to bid truthfully. We study two related problems concerning the VCG mechanism: the problem of revenue guarantees, and that of collusion. The existence of these problems even in oneitem settings is wellknown; in this paper, we lay out their full extent in multiitem settings. We study four settings: combinatorial forward auctions with free disposal, combinatorial reverse auctions with free disposal, combinatorial forward (or reverse) auctions without free disposal, and combinatorial exchanges. In each setting, we give an example of how additional bidders (colluders) can make the outcome much worse (less revenue or higher cost) under the VCG mechanism (but not under a first price mechanism); derive necessary and sufficient conditions for such an effective collusion to be possible under the VCG mechanism; and (when nontrivial) study the computational complexity of deciding whether these conditions hold.
Mechanism design for fractional scheduling on unrelated machines
 Automata, Languages and Programming
, 2007
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Implementation with a bounded action space
 In Proceedings of the 7th ACM conference on Electronic commerce
, 2006
"... While traditional mechanism design typically assumes isomorphism between the agents’ type and action spaces, in many situations the agents face strict restrictions on their action space due to, e.g., technical, behavioral or regulatory reasons. We devise a general framework for the study of mechani ..."
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Cited by 14 (5 self)
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While traditional mechanism design typically assumes isomorphism between the agents’ type and action spaces, in many situations the agents face strict restrictions on their action space due to, e.g., technical, behavioral or regulatory reasons. We devise a general framework for the study of mechanism design in singleparameter environments with restricted action spaces. Our contribution is threefold. First, we characterize sufficient conditions under which the informationtheoretically optimal socialchoice rule can be implemented in dominant strategies, and prove that any multilinear socialchoice rule is dominantstrategy implementable with no additional cost. Second, we identify necessary conditions for the optimality of actionbounded mechanisms, and fully characterize the optimal mechanisms and strategies in games with two players and two alternatives. Finally, we prove that for any multilinear socialchoice rule, the optimal mechanism with k actions incurs an expected loss of O ( 1 k2) compared to the optimal mechanisms with unrestricted action spaces. Our results apply to various economic and computational settings, and we demonstrate their applicability to signaling games, publicgood models and routing in networks. 1
A characterization of 2player mechanisms for scheduling
, 2008
"... We study the mechanism design problem of scheduling unrelated machines and we completely characterize the decisive truthful mechanisms for two players when the domain contains both positive and negative values. We show that the class of truthful mechanisms is very limited: A decisive truthful mechan ..."
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Cited by 13 (5 self)
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We study the mechanism design problem of scheduling unrelated machines and we completely characterize the decisive truthful mechanisms for two players when the domain contains both positive and negative values. We show that the class of truthful mechanisms is very limited: A decisive truthful mechanism partitions the tasks into groups so that the tasks in each group are allocated independently of the other groups. Tasks in a group of size at least two are allocated by an affine minimizer and tasks in singleton groups by a taskindependent mechanism. This characterization is about all truthful mechanisms, including those with unbounded approximation ratio. A direct consequence of this approach is that the approximation ratio of mechanisms for two players is 2, even for two tasks. In fact, it follows that for two players, VCG is the unique algorithm with optimal approximation 2. This characterization provides some support that any decisive truthful mechanism (for 3 or more players) partitions the tasks into groups some of which are allocated by affine minimizers, while the rest are allocated by a threshold mechanism (in which a task is allocated to a player when it is below a threshold value which depends only on the values of the other players). We also show here that the class of threshold mechanisms is identical to the class of additive mechanisms.
A lower bound of 1+φ for truthful scheduling mechanisms
 In The Proc. of the 32nd International Symposium on Mathematical Foundations of Computer Science (MFCS
"... Abstract. We give an improved lower bound for the approximation ratio of truthful mechanisms for the unrelated machines scheduling problem. The mechanism design version of the problem which was proposed and studied in a seminal paper of Nisan and Ronen is at the core of the emerging area of Algorith ..."
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Cited by 13 (3 self)
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Abstract. We give an improved lower bound for the approximation ratio of truthful mechanisms for the unrelated machines scheduling problem. The mechanism design version of the problem which was proposed and studied in a seminal paper of Nisan and Ronen is at the core of the emerging area of Algorithmic Game Theory. The new lower bound 1 + φ ≈ 2.618 is a step towards the final resolution of this important problem. 1