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On the hardness of being truthful
 In Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS
"... Abstract The central problem in computational mechanism design is the tension between incentive compatibility and computational ef ciency. We establish the rst significant approximability gap between algorithms that are both truthful and computationallyef cient, and algorithms that only achieve on ..."
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Cited by 63 (8 self)
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Abstract The central problem in computational mechanism design is the tension between incentive compatibility and computational ef ciency. We establish the rst significant approximability gap between algorithms that are both truthful and computationallyef cient, and algorithms that only achieve one of these two desiderata. This is shown in the context of a novel mechanism design problem which we call the COMBINATORIAL PUBLIC PROJECT PROBLEM (CPPP). CPPP is an abstraction of many common mechanism design situations, ranging from elections of kibbutz committees to network design. Our computationalcomplexity result is one of the rst impossibility results connecting mechanism design to complexity theory; its novel proof technique involves an application of the SauerShelah Lemma and may be of wider applicability, both within and without mechanism design.
How hard is it to approximate the best Nash equilibrium?
, 2009
"... The quest for a PTAS for Nash equilibrium in a twoplayer game seeks to circumvent the PPADcompleteness of an (exact) Nash equilibrium by finding an approximate equilibrium, and has emerged as a major open question in Algorithmic Game Theory. A closely related problem is that of finding an equilibri ..."
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Cited by 31 (0 self)
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The quest for a PTAS for Nash equilibrium in a twoplayer game seeks to circumvent the PPADcompleteness of an (exact) Nash equilibrium by finding an approximate equilibrium, and has emerged as a major open question in Algorithmic Game Theory. A closely related problem is that of finding an equilibrium maximizing a certain objective, such as the social welfare. This optimization problem was shown to be NPhard by Gilboa and Zemel [Games and Economic Behavior 1989]. However, this NPhardness is unlikely to extend to finding an approximate equilibrium, since the latter admits a quasipolynomial time algorithm, as proved by Lipton, Markakis and Mehta [Proc. of 4th EC, 2003]. We show that this optimization problem, namely, finding in a twoplayer game an approximate equilibrium achieving large social welfare is unlikely to have a polynomial time algorithm. One interpretation of our results is that the quest for a PTAS for Nash equilibrium should not extend to a PTAS for finding the best Nash equilibrium, which stands in contrast to certain algorithmic techniques used so far (e.g. sampling and enumeration). Technically, our result is a reduction from a notoriously difficult problem in modern Combinatorics, of finding a planted (but hidden) clique in a random graph G(n, 1/2). Our reduction starts from an instance with planted clique size k = O(log n). For comparison, the currently known algorithms due to Alon, Krivelevich and Sudakov [Random Struct. & Algorithms, 1998], and Krauthgamer and Feige [Random Struct. & Algorithms, 2000], are effective for a much larger clique size k = Ω(√n).
Characterizing truthful multiarmed bandit mechanisms
 In ACMEC
, 2009
"... We consider a multiround auction setting motivated by payperclick auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. I ..."
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Cited by 30 (1 self)
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We consider a multiround auction setting motivated by payperclick auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. Initially, neither the auctioneer nor the advertisers have any information about the likelihood of clicks on the advertisements. The auctioneer’s goal is to design a (dominant strategies) truthful mechanism that (approximately) maximizes the social welfare. If the advertisers bid their true private values, our problem is equivalent to the multiarmed bandit problem, and thus can be viewed as a strategic version of the latter. In particular, for both problems the quality of an algorithm can be characterized by regret, the difference in social welfare between the algorithm and the benchmark which always selects the same“best”advertisement. We investigate how the design of multiarmed bandit algorithms is affected by the restriction that the resulting mechanism must be truthful. We find that truthful mechanisms have certain strong structural properties – essentially, they must separate exploration from exploitation – and they incur much higher regret than the optimal multiarmed bandit algorithms. Moreover, we provide a truthful mechanism which (essentially) matches our lower bound on regret.
VC v. VCG: Inapproximability of combinatorial auctions via generalizations of the VC dimension
 CoRR
"... The existence of incentivecompatible computationallyefficient protocols for combinatorial auctions with decent approximation ratios is the paradigmatic problem in computational mechanism design. It is believed that in many cases good approximations for combinatorial auctions may be unattainable du ..."
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The existence of incentivecompatible computationallyefficient protocols for combinatorial auctions with decent approximation ratios is the paradigmatic problem in computational mechanism design. It is believed that in many cases good approximations for combinatorial auctions may be unattainable due to an inherent clash between truthfulness and computational efficiency. However, to date, researchers lack the machinery to prove such results. In this paper, we present a new approach: We take the first steps towards the development of new technologies for lower bounding the VCdimension of ktuples of disjoint sets. We apply this machinery to prove the first computationalcomplexity inapproximability results for incentivecompatible mechanisms for combinatorial auctions. These results hold for the important class of VCGbased mechanisms, and are based on the complexity assumption that NP has no polynomialsize circuits. We believe that our approach holds great promise. Indeed, subsequently to our work, Buchfuhrer and Umans [10], and, independently, Dughmi et al. [20], strengthened our results via extensions of our techniques, thus proving conjectures we presented in [32]
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"... Abstract In this lecture we give a brief introduction to the field of Algorithmic Game Theory ..."
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Abstract In this lecture we give a brief introduction to the field of Algorithmic Game Theory
Selfish Bin Covering
, 2009
"... In this paper, we address for the first time the selfish bin covering problem, which is greatly related both to the famous bin covering problem in the field of combinatorial optimization, and to the classic weighted majority game in coalitional game theory. As in the other models of algorithmic ga ..."
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In this paper, we address for the first time the selfish bin covering problem, which is greatly related both to the famous bin covering problem in the field of combinatorial optimization, and to the classic weighted majority game in coalitional game theory. As in the other models of algorithmic game theory, what we mainly concern in this model is how the decentralized decision making affects the social profit. Besides the standard PoA and PoS, which are based on Nash equilibrium, we also take into account the strong Nash equilibrium, and define several new equilibria. For each equilibrium, the corresponding PoA and PoS are given. The problem of computing an equilibrium, as well as computing a good one (in the sense that with a large social profit), is also considered.