ArcherTardos - Truthful Mechanisms for One-Parameter Agents...

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Truthful Mechanisms for One-Parameter Agents Aaron Archer ´ Eva Tardos Abstract 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 combinato- rial optimization to which the celebrated VCG mechanism does not apply. For scheduling related parallel machines ( ), we give a 3-approximation mechanism based on randomized rounding of the optimal fractional solution. This problem is NP-complete, and the standard approxima- tion algorithms (greedy load-balancing or the PTAS) can- not be used in truthful mechanisms. We show our mecha- nism 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, (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 (minimizing the weighted sum of completion times), we prove a lower bound of for the best approximation ratio achievable by a truthful mechanism. 1 Introduction In economics, social choice theory addresses the prob- lem of aggregating individuals’ preferences to make a group Operations Research Department, Cornell University, Ithaca, NY 14853. Email: . Supported by the Fannie and John Hertz Foundation. Computer Science Department, Cornell University, Ithaca, NY 14853. Email: Research supported in part by NSF grant CCR-9700163 and ONR grant N00014-98-1-0589. decision. As indicated by Arrow’s impossibility theorem for satisfactory voting systems [2], this is a thorny problem. It is further complicated by the possibility that the partici- pants (usually called players or agents ) might try to manip- ulate the system by misrepresenting their preferences. The field of mechanism design recognizes this game theoretic aspect and aims to arrange things so that a rational player will never find it in her self-interest to lie. Mechanisms that do this are called strategyproof or truthful . Because of some stifling negative results that apply when the agents’ preferences can be arbitrary, it is common to re- strict the domain of preferences by assuming additive sepa- rability . Each agent is assumed to incur some intrinsic ben- efit or loss (called its valuation ) depending on the outcome of the mechanism, and this valuation is expressible in some
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This note was uploaded on 12/08/2011 for the course CIS 620 taught by Professor Cis620 during the Fall '08 term at UPenn.

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ArcherTardos - Truthful Mechanisms for One-Parameter Agents...

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