## Truthful randomized mechanisms for combinatorial auctions (2006)

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Venue: | IN STOC |

Citations: | 79 - 15 self |

### BibTeX

@INPROCEEDINGS{Dobzinski06truthfulrandomized,

author = {Shahar Dobzinski and Noam Nisan and Michael Schapira},

title = {Truthful randomized mechanisms for combinatorial auctions},

booktitle = {IN STOC},

year = {2006},

pages = {644--652},

publisher = {}

}

### Years of Citing Articles

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### Abstract

We design two computationally-efficient incentive-compatible mechanisms for combinatorial auctions with general bidder preferences. Both mechanisms are randomized, and are incentive-compatible in the universal sense. This is in contrast to recent previous work that only addresses the weaker notion of incentive compatibility in expectation. The first mechanism obtains an O(pm)-approximation of the optimal social welfare for arbitrary bidder valuations -- this is the best approximation possible in polynomial time. The second one obtains an O(log2 m)- approximation for a subclass of bidder valuations that includes all submodular bidders. This improves over the best previously obtained incentive-compatible mechanism for this class which only provides an O(pm)-approximation.

### Citations

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Citation Context ...king at both issues - strategic and algorithmic - together. For an introduction see [20]. The basic strategic notions are taken from the field of mechanism design - a subfield of economic theory (see =-=[18, 23]-=-), and in most of the work in computational settings, as in this one, the very robust notion of equilibrium in dominant strategies is used. It is well known ([18], see [20]) that without loss of gener... |

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Citation Context ...pants are always rationally motivated to correctly report their private information. The main difficulty in this field is the fact that the basic technique of mechanism design – namely VCG mechanisms =-=[25, 4, 11]-=- – can only be applied in cases where the exact optimal outcome is achieved. However, in most interesting computational applications, exact optimization is NP-hard, and computationally-speaking we mus... |

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Citation Context ...pants are always rationally motivated to correctly report their private information. The main difficulty in this field is the fact that the basic technique of mechanism design – namely VCG mechanisms =-=[25, 4, 11]-=- – can only be applied in cases where the exact optimal outcome is achieved. However, in most interesting computational applications, exact optimization is NP-hard, and computationally-speaking we mus... |

556 | 2001): “Algorithmic mechanism design
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Citation Context ...cy considerations. Target applications include many types of protocols for Internet environment that necessitate looking at both issues - strategic and algorithmic - together. For an introduction see =-=[20]-=-. The basic strategic notions are taken from the field of mechanism design - a subfield of economic theory (see [18, 23]), and in most of the work in computational settings, as in this one, the very r... |

515 | Algorithm for Optimal Winner Determination in Combinatorial Auctions
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Citation Context ...mann et al [17] were able to design an incentive-compatible, efficientlycomputable, approximation mechanism – which achieves an approximation ratio that is as good as computationally possible Θ( √ m) =-=[24]-=- – for the special case of “single-minded bidders”. This is the case in which each bidder is only interested in a single bundle of goods. For this special case, as well as some other single-parameter ... |

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Citation Context ...rnative incentivecompatible mechanisms for interesting applications. The problem of combinatorial auctions has gained the status of the paradigmatic problem of this field. For a thorough overview see =-=[5]-=-. In a combinatorial auction, m items are auctioned to n players. Each player i has a valuation function vi that describes his value vi(S) for each subset ∗ The School of Computer Science and Engineer... |

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Citation Context ...king at both issues - strategic and algorithmic - together. For an introduction see [20]. The basic strategic notions are taken from the field of mechanism design - a subfield of economic theory (see =-=[18, 23]-=-), and in most of the work in computational settings, as in this one, the very robust notion of equilibrium in dominant strategies is used. It is well known ([18], see [20]) that without loss of gener... |

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Citation Context ...e is achieved. However, in most interesting computational applications, exact optimization is NP-hard, and computationally-speaking we must settle for approximations or heuristics. As was observed in =-=[20, 17]-=-, the VCG technique cannot be applied in such cases, and in fact [21] showed that this inapplicability was essentially universal. Thus, the challenge is to design alternative incentivecompatible mecha... |

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Citation Context ...pants are always rationally motivated to correctly report their private information. The main difficulty in this field is the fact that the basic technique of mechanism design - namely VCG mechanisms =-=[25, 4, 11]-=- - can only be applied in cases where the exact optimal outcome is achieved. However, in most interesting computational applications, exact optimization is NP-hard, and computationally-speaking we mus... |

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Citation Context ...h good and indeed is not a VCG mechanism. Some evidence showing that obtaining a non-VCG incentive-compatible mechanism for combinatorial auctions and related problems would be difficult was given in =-=[14]-=-. 1.2 Randomized Mechanisms It was observed in [20] that randomized mechanisms can sometimes provide better approximation ratios than deterministic ones. There are two possible definitions for incenti... |

104 | An approximate truthful mechanism for combinatorial auctions with single parameter agents
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Citation Context ...terested in a single bundle of goods. For this special case, as well as some other single-parameter scenarios a host of incentive compatible mechanisms have been designed in the last few years (e.g., =-=[19, 1, 10, 9]-=-). However, almost nothing is known for more general cases in which bidders have complex multi-dimensional preferences. Only two results are known in multi-dimensional settings1: the first is a pair o... |

92 | Approximation algorithms for combinatorial auctions with complement-free bidders
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Citation Context ..., even for the most interesting special cases, but several approximation algorithms, with varying approximation ratios, are known for the general case as well as for various interesting special cases =-=[16, 6, 7, 8]-=-. However, these approximation algorithms do not yield incentive compatible mechanisms. In a landmark paper, Lehmann et al [17] were able to design an incentive-compatible, efficientlycomputable, appr... |

90 | Incentive compatible multi unit combinatorial auctions
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Citation Context ...of O(m/plog m) for the general case [12] and a weak O(pm) for the "complement-free" case [6] - both ratios being quite far from what is computationally possible. The second result is the mechanism of =-=[2]-=- that applies only to the special case of auctions with many duplicates of each good and indeed is not a VCG mechanism. Some evidence showing that obtaining a non-VCG incentive-compatible mechanism fo... |

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Citation Context ...on of the bidders have many properties in common (e.g., both hold a constant fraction of the total welfare.) This idea is similar to the main principle in random-sampling auctions for "digital goods" =-=[10, 9]-=-. However, our situation is much more complex due to the multi-parameter setting of combinatorial auctions, in contrast to the single-parameter setting of [10, 9]. In addition, our goal is to optimize... |

85 | Truthful and near-optimal mechanism design via linear programming
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Citation Context ...ion only requires that players maximize their expected utility, where the expectation is over the random choices of the mechanism (but still for every behavior of the other players). This was used in =-=[15, 8]-=- (see below), and will be called incentive compatibility in expectation. There are two major implications of the difference between these two notions: 1. Attitude towards risk: randomized mechanisms t... |

74 |
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Citation Context ...pants are always rationally motivated to correctly report their private information. The main difficulty in this field is the fact that the basic technique of mechanism design – namely VCG mechanisms =-=[25, 4, 11]-=- – can only be applied in cases where the exact optimal outcome is achieved. However, in most interesting computational applications, exact optimization is NP-hard, and computationally-speaking we mus... |

66 |
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(Show Context)
Citation Context ...e is achieved. However, in most interesting computational applications, exact optimization is NP-hard, and computationally-speaking we must settle for approximations or heuristics. As was observed in =-=[20, 17]-=-, the VCG technique cannot be applied in such cases, and in fact [21] showed that this inapplicability was essentially universal. Thus, the challenge is to design alternative incentivecompatible mecha... |

47 |
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Citation Context ...pants are always rationally motivated to correctly report their private information. The main difficulty in this field is the fact that the basic technique of mechanism design - namely VCG mechanisms =-=[25, 4, 11]-=- - can only be applied in cases where the exact optimal outcome is achieved. However, in most interesting computational applications, exact optimization is NP-hard, and computationally-speaking we mus... |

37 | Inapproximability results for combinatorial auctions with submodular utility functions
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Citation Context ...torial auctions have recently received great attention. In particular, combinatorial auctions in which all bidders are known to have submodular valuations are the subject of extensive research (e.g., =-=[16, 6, 13, 7]-=-). A valuation v is submodular if v(S [T )+v(S "T ) <= v(S) + v(T ) for all S, T ` M . All submodular valuations are known to be strictly contained in the more general class of valuations termed "XOS"... |

24 |
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Citation Context ...xact optimization is NP-hard, and computationally-speaking we must settle for approximations or heuristics. As was observed in [20, 17], the VCG technique cannot be applied in such cases, and in fact =-=[21]-=- showed that this inapplicability was essentially universal. Thus, the challenge is to design alternative incentivecompatible mechanisms for interesting applications. The problem of combinatorial auct... |

23 |
Nisan and Amir Ronen. Algorithmic mechanism design
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Citation Context ...cy considerations. Target applications include many types of protocols for Internet environment that necessitate looking at both issues – strategic and algorithmic – together. For an introduction see =-=[20]-=-. The basic strategic notions are taken from the field of mechanism design – a subfield of economic theory (see [18, 23]), and in most of the work in computational settings, as in this one, the very r... |

21 | Microeconomic theory, Oxford University Press. 144 Mirrlees - MasCollel, Whinston, et al. - 1995 |

18 |
On maximizing welfare where the utility functions are subadditive
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Citation Context ..., even for the most interesting special cases, but several approximation algorithms, with varying approximation ratios, are known for the general case as well as for various interesting special cases =-=[16, 6, 7, 8]-=-. However, these approximation algorithms do not yield incentive compatible mechanisms. In a landmark paper, Lehmann et al [17] were able to design an incentive-compatible, efficientlycomputable, appr... |

17 | On the computational power of iterative auctions I: demand queries, Discussion paper no. 381, The Center for the Study of Rationality, The Hebrew University., An extended abstract in EC’05 contained preliminary results
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(Show Context)
Citation Context ... the natural parameters of the problem: the number of players n and the number of items m. Access to the (exponentially long) valuation functions of the players is done using the usual demand queries =-=[3, 6, 7]-=-, in which bidders are presented with a vector of item prices p1...pm and reply with the set of items S that maximizes their utility under these prices v(S) - Pj2S pj. The approximation factor mention... |

15 |
Bundling equilibrium in combinatrial auctions
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Citation Context ... completely optimize over a very restricted range of allocations and then use the usual VCG mechanism. These get a barely better than trivial approximation ratio of O(m/ √ log m) for the general case =-=[12]-=- and a weak O( √ m) for the “complement-free” case [6] – both ratios being quite far from what is computationally possible. The second result is the mechanism of [2] that applies only to the special c... |

9 |
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(Show Context)
Citation Context ...pants are always rationally motivated to correctly report their private information. The main difficulty in this field is the fact that the basic technique of mechanism design - namely VCG mechanisms =-=[25, 4, 11]-=- - can only be applied in cases where the exact optimal outcome is achieved. However, in most interesting computational applications, exact optimization is NP-hard, and computationally-speaking we mus... |