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Approximate Mechanism Design Without Money
, 2009
"... The literature on algorithmic mechanism design is mostly concerned with gametheoretic versions of optimization problems to which standard economic moneybased mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on enforc ..."
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The literature on algorithmic mechanism design is mostly concerned with gametheoretic versions of optimization problems to which standard economic moneybased mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on enforcing payments. In this paper, we advocate the reconsideration of highly structured optimization problems in the context of mechanism design. We explicitly argue for the first time that, in such domains, approximation can be leveraged to obtain truthfulness without resorting to payments. This stands in contrast to previous work where payments are ubiquitous, and (more often than not) approximation is a necessary evil that is required to circumvent computational complexity. We present a case study in approximate mechanism design without money. In our basic setting agents are located on the real line and the mechanism must select the location of a public facility; the cost of an agent is its distance to the facility. We establish tight upper and lower bounds for the approximation ratio given by strategyproof mechanisms without payments, with respect to both deterministic and randomized mechanisms, under two objective functions: the social cost, and the maximum cost. We then extend our results in two natural directions: a domain where two facilities must be located, and a domain where each agent controls multiple locations.
Mix and Match
, 2010
"... Consider a matching problem on a graph where disjoint sets of vertices are privately owned by selfinterested agents. An edge between a pair of vertices indicates compatibility and allows the vertices to match. We seek a mechanism to maximize the number of matches despite selfinterest, with agents ..."
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Cited by 25 (9 self)
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Consider a matching problem on a graph where disjoint sets of vertices are privately owned by selfinterested agents. An edge between a pair of vertices indicates compatibility and allows the vertices to match. We seek a mechanism to maximize the number of matches despite selfinterest, with agents that each want to maximize the number of their own vertices that match. Each agent can choose to hide some of its vertices, and then privately match the hidden vertices with any of its own vertices that go unmatched by the mechanism. A prominent application of this model is to kidney exchange, where agents correspond to hospitals and vertices to donorpatient pairs. Here hospitals may game an exchange by holding back pairs and harm social welfare. In this paper we seek to design mechanisms that are strategyproof, in the sense that agents cannot benefit from hiding vertices, and approximately maximize efficiency, i.e., produce a matching that is close in cardinality to the maximum cardinality matching. Our main result is the design and analysis of the eponymous MixandMatch mechanism; we show that this randomized mechanism is strategyproof and provides a 2approximation. Lower bounds establish that the mechanism is near optimal.
Social Welfare in Onesided Matching Markets without Money
"... We study social welfare in onesided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments. We consider two na ..."
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Cited by 7 (0 self)
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We study social welfare in onesided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments. We consider two natural measures of social welfare: the ordinal welfare factor which measures the number of agents that are at least as happy as in some unknown, arbitrary benchmark allocation, and the linear welfare factor which assumes an agent’s utility linearly decreases down his preference lists, and measures the total utility to that achieved by an optimal allocation. We analyze two matching mechanisms which have been extensively studied by economists. The first mechanism is the random serial dictatorship (RSD) where agents are ordered in accordance with a randomly chosen permutation, and are successively allocated their best choice among the unallocated items. The second mechanism is the probabilistic serial (PS) mechanism of Bogomolnaia and Moulin [8], which computes a fractional allocation that can be expressed as a convex combination of integral allocations. The welfare factor of a mechanism is the infimum over all instances. For RSD, we show that the ordinal welfare factor is asymptotically 1/2, while the linear welfare factor lies in the interval [.526, 2/3]. For PS, we show that the ordinal welfare factor is also 1/2 while the linear welfare factor is roughly 2/3. To our knowledge, these results are the first nontrivial performance guarantees for these natural mechanisms.
Tight bounds for strategyproof classification
 In Proc. of 10th AAMAS
, 2011
"... Strategyproof (SP) classification considers situations in which a decisionmaker must classify a set of input points with binary labels, minimizing expected error. Labels of input points are reported by selfinterested agents, who may lie so as to obtain a classifier more closely matching their own ..."
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Cited by 2 (2 self)
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Strategyproof (SP) classification considers situations in which a decisionmaker must classify a set of input points with binary labels, minimizing expected error. Labels of input points are reported by selfinterested agents, who may lie so as to obtain a classifier more closely matching their own labels. These lies would create a bias in the data, and thus motivate the design of truthful mechanisms that discourage false reporting. We here answer questions left open by previous research on strategyproof classification [12, 13, 14], in particular regarding the best approximation ratio (in terms of social welfare) that an SP mechanism can guarantee for n agents. Our primary result is a lower bound of 3 − 2 on the approximation ratio of SP mechanisms under n the shared inputs assumption; this shows that the previously known upper bound (for uniform weights) is tight. The proof relies on a result from Social Choice theory, showing that any SP mechanism must select a dictator at random, according to some fixed distribution. We then show how different randomizations can improve the best known mechanism when agents are weighted, matching the lower bound with a tight upper bound. These results contribute both to a better understanding of the limits of SP classification, as well as to the development of similar tools in other, related domains such as SP facility location.
B.: Truthful mechanism design via correlated tree rounding
 In: Proceedings of the 16th ACM conference on Electronic commerce, ACM (2015
"... One of the most powerful algorithmic techniques for truthful mechanism design are maximalindistributionalrange (MIDR) mechanisms. Unfortunately, many algorithms using this paradigm rely on heavy algorithmic machinery and require the ellipsoid method or (approximate) solution of convex programs. ..."
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One of the most powerful algorithmic techniques for truthful mechanism design are maximalindistributionalrange (MIDR) mechanisms. Unfortunately, many algorithms using this paradigm rely on heavy algorithmic machinery and require the ellipsoid method or (approximate) solution of convex programs. In this paper, we present a simple and natural correlated rounding technique for designing mechanisms that are truthful in expectation. Our technique is elementary and can be implemented quickly. The main property we rely on is that the domain offers fractional optimum solutions with a tree structure. In auctions based on the generalized assignment problem, each bidder has a publicly known knapsack constraint that captures the subsets of items that are of value to him. He has a private valuation for each item and strives to maximize the value of assigned items minus payment. For this domain we design a mechanism for social welfare maximization. Our technique gives a truthful 2approximate MIDR mechanism without using the ellipsoid method or convex programming. In contrast to some previous work, our mechanism achieves exact truthfulness. In restrictedrelated scheduling with selfish machines, each job comes with a public weight, and it must be assigned to a machine from a public jobspecific subset. Each machine has a private speed and strives to maximize payments minus workload of jobs assigned to it. For this domain we design a mechanism
Strategyproof Facility Location and the Least Squares Objective
"... We consider the problem of locating a public facility on a tree, where a set of n strategic agents report their locations and a mechanism determines, either deterministically or randomly, the location of the facility. The contribution of this paper is twofold. First, we introduce, for the first time ..."
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We consider the problem of locating a public facility on a tree, where a set of n strategic agents report their locations and a mechanism determines, either deterministically or randomly, the location of the facility. The contribution of this paper is twofold. First, we introduce, for the first time, a general and clean family of strategyproof (SP) mechanisms for facility location on tree networks. Quite miraculously, all of the deterministic and randomized SP mechanisms that have been previously proposed can be cast as special cases of this family. Thus, the proposed mechanism unifies much of the existing literature on SP facility location problems, and simplifies its analysis. Second, we demonstrate the strength of the proposed family of mechanisms by proving new bounds on the approximation of the minimum sum of squares (miniSOS) objective on line and tree networks. For lines, we devise a randomized mechanism that gives 1.5approximation, and show, through a subtle analysis, that no other randomized SP mechanism can provide a better approximation. For general trees, we construct a randomized mechanism that gives 1.83approximation. This result provides a separation between deterministic and randomized mechanisms, as it is complemented by a lower bound of 2 for any deterministic mechanism. We believe that the devised family of mechanisms will prove useful in studying approximation bounds for additional objectives.
C.: Combinatorial auctions without money
 In: Proceedings of the 2014 international conference on Autonomous agents and multiagent systems, International Foundation for Autonomous Agents and Multiagent Systems
, 2014
"... ar ..."
Verifiably Truthful Mechanisms
"... It is typically expected that if a mechanism is truthful, then the agents would, indeed, truthfully report their private information. But why would an agent believe that the mechanism is truthful? We wish to design truthful mechanisms that are “simple”, that is, whose truthfulness can be verified ..."
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It is typically expected that if a mechanism is truthful, then the agents would, indeed, truthfully report their private information. But why would an agent believe that the mechanism is truthful? We wish to design truthful mechanisms that are “simple”, that is, whose truthfulness can be verified efficiently (in the computational sense). Our approach involves three steps: (i) specifying the structure of mechanisms, (ii) constructing a verification algorithm, and (iii) measuring the quality of verifiably truthful mechanisms. We demonstrate this approach using a case study: approximate mechanism design without money for facility location.
Truthful Mechanism Design without Money: No Upward Bidding
"... Abstract. GibbardSatterthwaite (GS) theorem rules out the existence of any truthful, nondictatorial and unanimous social choice function whose range comprises three or more alternatives. To circumvent the GS impossibility, researchers have introduced restricted domains with additional assumption ..."
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Abstract. GibbardSatterthwaite (GS) theorem rules out the existence of any truthful, nondictatorial and unanimous social choice function whose range comprises three or more alternatives. To circumvent the GS impossibility, researchers have introduced restricted domains with additional assumptions to admit truthful mechanisms. We follow this line of research and look at a setting in which a set of items has to be assigned to a set of agents and transfer of money is not allowed. Agents have private cardinal valuations over packages of items. Agents are selfish and may report wrong valuations in order to maximize their utility which is to achieve a package of higher valuation. Our goal is to find a nondictatorial and truthful mechanism optimizing social welfare. We eliminate the possibility of upward bidding. The assumption of no upward bidding may seem strong, nevertheless we argue that finding a truthful mechanism for this setting falls under the GS impossibility. Consequently, we analyze the problem with additional assumptions such as small markets with identical items, singleparameter valuations and variations of the generalized assignment problem and show truthful and nondictatorial mechanisms for these settings.