We consider algorithmic problems in a distributed setting where the participants cannot be assumed to follow the algorithm but rather their own self-interest. As such participants, termed agents, are capable of manipulating the algorithm, the algorithm designer should ensure in advance that the agents ’ interests are best served by behaving correctly. Following notions from the field of mechanism design, we suggest a framework for studying such algorithms. Our main technical contribution concerns the study of a representative task scheduling problem for which the standard mechanism design tools do not suffice. Journal of Economic Literature

One of the major achievements of mechanism design theory is the family of truthful (incentive compatible) mechanisms often called VCG (named after Vickrey, Clarke and Groves). When applying VCG mechanisms to complex mechanism design problems such as combinatorial auctions a problem emerges: even finding optimal outcomes is computationally intractable. A striking observation is that if the optimal outcome is replaced by the results of computationally tractable approximation algorithms or heuristics then the resulting mechanism (termed VCG-based) is no longer necessarily truthful! The first part of this paper considers this problem in depth and shows that it is almost 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 non-truthful VCG-based mechanisms. The second part of this paper proposes a method for handling this non-truthfulness. We introduce a...

Many recent applications of interest involve self-interested participants. As such participants, termed agents, may manipulate the algorithm for their own benefit, a new challenge emerges: The design of algorithms and protocols that perform well when the agents behave according to their own self-interest. This led several researchers to consider computational models that are based on a sub-field of game-theory and micro-economics called mechanism design. This paper introduces this topic mainly through examples. It demonstrates that in many cases selfishness can be satisfactorily overcome, surveys some of the recent trends in this area and presents new challenging problems. The paper is mostly based on classic results from mechanism design as well as on recent work by the author and others.

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We study a generic task allocation problem called shortest paths: Let G be a directed graph in which the edges are owned by self interested agents. Each edge has an associated cost that is privately known to its owner. Let s and t be two distinguished nodes in G. Given a distribution on the edge costs, the goal is to design a mechanism (protocol) which acquires a cheap s-t path. We first prove that the class of generalized VCG mechanisms has certain monotonicity properties. We exploit this observation to obtain, under an independence assumption, expected payments which are significantly better than the worst case bounds of [4, 7]. We then investigate whether these payments can be improved when there is a competition among paths. Surprisingly, we give evidence to the fact that typically such competition hardly helps incentive compatible mechanisms. In particular, we show this for the celebrated VCG mechanism. We then construct a novel general protocol combining the advantages of incentive compatible and non-incentive compatible mechanisms. Under reasonable assumptions on the agents we show that the overpayment of our mechanism is very small. Finally, we demonstrate that many task allocation problems can be reduced to shortest paths. 1

We consider computationally-efficient incentive-compatible mechanisms that use the VCG payment scheme, and study how well they can approximate the social welfare in auction settings. We present a novel technique for setting lower bounds on the approximation ratio of this type of mechanisms. Specifically, for combinatorial auctions among submodular (and thus also subadditive) bidders we prove an Ω(m 1 6) lower bound, which is close to the known upper bound of O(m 1 2), and qualitatively higher than the constant factor approximation possible from a purely computational point of view.

A major achievement of mechanism design theory is the family of truthful mechanisms often called VCG (named after Vickrey, Clarke and Groves). Although these mechanisms have many appealing properties, their essential intractability prevents them from being applied to complex problems like combinatorial auctions. In particular, VCG mechanisms require the agents to fully describe their valuation functions to the mechanism. Such a description may require exponential size and thus be infeasible for the agents. A natural approach for this problem is to introduce an intermediate language for the description of the valuations. Such a language must be succinct to both the agents and the mechanism. Unfortunately, the resulting mechanisms are neither truthful nor do they satisfy individual rationality. This paper suggests a general method for overcoming this difficulty. Given an intermediate language and an algorithm for computing the results, we propose three different mechanisms, each more powerful than its predecessor, but also more time consuming. Under reasonable assumptions, the results of our mechanisms are at least as good as the results of the algorithm on the actual valuations. All of our mechanisms have polynomial computational time and satisfy individual rationality.

Abstract. We study the scheduling problem on unrelated machines in the mechanism design setting. This problem was proposed and studied in the seminal paper of Nisan and Ronen [NR99], where they gave a 1.75-approximation randomized truthful mechanism for the case of two machines. We improve this result by a 1.6737-approximation randomized truthful mechanism. We also generalize our result to a 0.8368m-approximation mechanism for task scheduling with m machines, which improve the previous best upper bound of 0.875m[MS07].

September 2006This work was carried out under the supervision of

We study the problem of procuring a cheap path in a graph in which the edges are owned by selfinterested agents. We focus on basic properties of a class of generalized Vickrey-Clarke mechanisms for the problem. We show that this class of mechanisms satisfies a monotonicity property that can be used to achieve expected payments which, under certain independence assumption, are significantly better than the worst case bounds known for the problem. Next, we investigate whether these payments can be improved when there is competition among paths. Surprisingly, we give evidence to the fact that in many cases of interest such competition hardly helps incentive compatible mechanisms. In particular, we show this for the celebrated Vickrey-Clarke mechanism. We then propose a general method that combines the advantages of incentive compatible and non-incentive compatible mechanisms. Under some natural assumptions on the agents we show that the expected payment of our mechanisms is very small. Finally, we show that a wide range of task allocation problems can be reduced to the problem we study.