When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness). We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann O’Callaghan, and Shoham, who presented greedy heuristics. We show how to use IF-THEN-ELSE constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios. 1

Abstract This paper considers algorithmic problems in a distributed setting where the participants cannot be assumed to follow the algorithm but rather their own self-interest. Such scenarios arise, in particular, when computers or users aim to cooperate or trade over the Internet. 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. This exposition presents a model to formally study such algorithms. This model, based on the field of mechanism design, is taken from the author's joint work with Amir Ronen, and is similar to approaches taken in the distributed AI community in recent years. Using this model, we demonstrate how some of the techniques of mechanism design can be applied towards distributed computation problems. We then exhibit some issues that arise in distributed computation which require going beyond the existing theory of mechanism design. 1 Introduction A large part of research in computer science is concerned with protocols and algorithms for inter-connected collections of computers. The designer of such an algorithm or protocol always makes an implicit assumption that the participating computers will act as instructed- except, perhaps, for the faulty or malicious ones.

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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

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Many centralized two-sided markets form a matching between participants by running a stable marriage algorithm. It is a well-known fact that no matching mechanism based on a stable marriage algorithm can guarantee truthfulness as a dominant strategy for participants. However, as we will show in this paper, in a probabilistic setting where the preference lists of one side of the market are composed of only a constant (independent of the the size of the market) number of entries, each drawn from an arbitrary distribution, the number of participants that have more than one stable partner is vanishingly small. This proves (and generalizes) a conjecture of Roth and Peranson [23]. As a corollary Ó of this result, we show that, with high probability, the truthful strategy is the best response for a given player when the other players are truthful. We also analyze equilibria of the deferred acceptance stable marriage game. We show that the game with complete information has an equilibrium in which a fraction of the strategies are truthful in expectation. In the more realistic setting of a game of incomplete information, we will show that the set of truthful strate-gies form a Ó

In many settings, agents participating in mechanisms do not know their preferences a priori. Instead, they must actively determine them through deliberation (e.g., information processing or information gathering). Agents are faced not only with the problem of deciding how to reveal their preferences to the mechanism but also how to deliberate in order to determine their preferences. For such settings, we have introduced the deliberation equilibrium as the game-theoretic solution concept where the agents ’ deliberation actions are modeled as part of their strategies. In this paper, we lay out mechanism design principles for such deliberative agents. We also derive the first impossibility results for such settings- specifically for private-value auctions where the agents ’ utility functions are quasilinear, but the agents can only determine their valuations through deliberation. We propose a set of intuitive properties which are desirable in mechanisms used among deliberative agents. First, mechanisms should be non-deliberative: the mechanism should not be solving the deliberation problems for the agents. Secondly, mechanisms should be deliberationproof: agents should not deliberate on others’ valuations in equilibrium. Third, the mechanism should be non-deceiving: agents do not strategically misrepresent. Finally, the mechanism should be sensitive: the agents’ actions should affect the outcome. We show that no direct-revelation mechanism satisfies these four properties. Moving beyond direct-revelation mechanisms, we show that no value-based mechanism (that is, mechanism where the agents are only asked to report valuations- either partially or fully determined ones) satisfies these four properties.

We consider the problem of designing truthful mechanisms to minimize the makespan on m unrelated machines. In their seminal paper, Nisan and Ronen [14] showed a lower bound of 2, and an upper bound of m, thus leaving a large gap. They conjectured that their upper bound is tight, but were unable to prove it. Despite many attempts that yield positive results for several special cases, the conjecture is far from being solved: the lower bound was only recently slightly increased to 2.61 [5, 10], while the best upper bound remained unchanged. In this paper we show the optimal lower bound on truthful anonymous mechanisms: no such mechanism can guarantee an approximation ratio better than m. This is the first concrete evidence to the correctness of the Nisan-Ronen conjecture, especially given that the classic scheduling algorithms are anonymous, and all state-of-the-art mechanisms for special cases of the problem are anonymous as well.

In Combinatorial Public Projects, there is a set of projects that may be undertaken, and a set of selfinterested players with a stake in the set of projects chosen. A public planner must choose a subset of these projects, subject to a resource constraint, with the goal of maximizing social welfare. Combinatorial Public Projects has emerged as one of the paradigmatic problems in Algorithmic Mechanism Design, a field concerned with solving fundamental resource allocation problems in the presence of both selfish behavior and the computational constraint of polynomial-time. We design a polynomial-time, truthful-in-expectation,(1−1/e)-approximation mechanism for welfare maximization in a fundamental variant of combinatorial public projects. Our results apply to combinatorial public projects when players have valuations that are matroid rank sums (MRS), which encompass most concrete examples of submodular functions studied in this context, including coverage functions, matroid weighted-rank functions, and convex combinations thereof. Our approximation factor is the best possible, assuming P ̸ = NP. Ours is the first mechanism that achieves a constant factor approximation for a natural NP-hard variant of combinatorial public projects.

In the presence of self-interested parties, mechanism designers typically aim to achieve their goals (or socialchoice functions) in an equilibrium. In this paper, we study the cost of such equilibrium requirements in terms of communication, a problem that was recently raised by Fadel and Segal [14]. While a certain amount of information x needs to be communicated just for computing the outcome of a certain social-choice function, an additional amount of communication may be required for computing the equilibrium-supporting prices (even if such prices are known to exist). Our main result shows that the total communication needed for this task can be greater than x by a factor linear in the number of players n, i.e., n · x. This is the first known lower bound for this problem. In fact, we show that this result holds even in single-parameter domains (under the common assumption that losing players pay zero). On the positive side, we show that certain classic economic objectives, namely, single-item auctions and public-good mechanisms, only entail a small overhead. Finally, we explore the communication overhead in welfare-maximization domains, and initiate the study of the overhead of computing payments that lie in the core of coalitional games. 1