## Truthful approximation mechanisms for restricted combinatorial auctions (2002)

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### BibTeX

@INPROCEEDINGS{Nisan02truthfulapproximation,

author = {Noam Nisan},

title = {Truthful approximation mechanisms for restricted combinatorial auctions},

booktitle = {},

year = {2002},

pages = {379--384}

}

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### Abstract

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

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Citation Context ...ipating agents are motivated to cooperate with the protocol 1. The basic algorithmic requirement is computational efficiency. Each of these requirements can be addressed separately: “VCG mechanisms” (=-=Vickrey 1961-=-; Clarke 1971; Groves 1973) – the basic possibility result of mechanism design – ensure truthfulness, and a host of algorithmic techniques (e.g. (Sandholm et al. 2001; Vohra & de Vries 2000; Zurel & N... |

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Citation Context ...tical purposes (despite the general NPhardness of the allocation problem). Unfortunately, these two requirements do conflict with each other! It has been noticed (Lehmann, O’Callaghan, & Shoham 1999; =-=Nisan & Ronen 1999-=-) that when VCG mechanisms are applied to non-optimal allocation algorithms (as any computationally efficient algorithm must be), truthfulness is not obtained. This problem was studied further in (Nis... |

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Citation Context ... for multi unit auctions. General Combinatorial Auctions The general combinatorial auction allocation problem is NPhard to approximate to within a factor of m 12− (for any fixed > 0) (Hastad 1999; =-=Sandholm 1999-=-; Lehmann, O’Callaghan, & Shoham 1999). A √m-approximation truthful mechanism is given in Lehmann, O’Callaghan, & Shoham for the case of single minded bidders. We narrow the gap between the upper boun... |

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Citation Context ...rs, agents) with differing goals. Many leading examples are motivated by Internet applications, e.g., various networking protocols, electronic commerce, and non-cooperative software agents. See e.g. (=-=Rosenschein & Zlotkin 1994-=-) for an early treatment, and (Nisan 1999; Papadimitriou 2001) for more recent surveys. The combinatorial auction problem is attaining this central status due to two elements: First, the problem is ve... |

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Citation Context ...999) that when VCG mechanisms are applied to non-optimal allocation algorithms (as any computationally efficient algorithm must be), truthfulness is not obtained. This problem was studied further in (=-=Nisan & Ronen 2000-=-; Monderer et al. 2001). The key positive result known so far is due to Lehmann, 1We defer the exact game theoretic definitions to section 2. In general one only needs equilibria, but the revelation p... |

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(Show Context)
Citation Context ... are motivated to cooperate with the protocol 1. The basic algorithmic requirement is computational efficiency. Each of these requirements can be addressed separately: “VCG mechanisms” (Vickrey 1961; =-=Clarke 1971-=-; Groves 1973) – the basic possibility result of mechanism design – ensure truthfulness, and a host of algorithmic techniques (e.g. (Sandholm et al. 2001; Vohra & de Vries 2000; Zurel & Nisan 2001)) c... |

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Citation Context ...he resulting, NP-hard, allocation problems, to pure game-theoretic questions of bidders’ strategies and equilibria. Much work has recently been done on these topics, see e.g., (Vohra & de Vries 2000; =-=Sandholm et al. 2001-=-; Nisan 2000; Lehmann, O’Callaghan, & Shoham 1999) and many references therein. Perhaps the most interesting questions are those that intimately combine computational considerations and game theoretic... |

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Citation Context ...echanisms are applied to non-optimal allocation algorithms (as any computationally efficient algorithm must be), truthfulness is not obtained. This problem was studied further in (Nisan & Ronen 2000; =-=Monderer et al. 2001-=-). The key positive result known so far is due to Lehmann, 1We defer the exact game theoretic definitions to section 2. In general one only needs equilibria, but the revelation principle allows concen... |

45 |
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Citation Context ...re motivated by Internet applications, e.g., various networking protocols, electronic commerce, and non-cooperative software agents. See e.g. (Rosenschein & Zlotkin 1994) for an early treatment, and (=-=Nisan 1999-=-; Papadimitriou 2001) for more recent surveys. The combinatorial auction problem is attaining this central status due to two elements: First, the problem is very expressive Copyright c© 2002, American... |

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2 |
Clique is hard to approximate to within n1−. Acta Mathematica 182
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(Show Context)
Citation Context ...ful mechanism for multi unit auctions. General Combinatorial Auctions The general combinatorial auction allocation problem is NPhard to approximate to within a factor of m 12− (for any fixed > 0) (=-=Hastad 1999-=-; Sandholm 1999; Lehmann, O’Callaghan, & Shoham 1999). A √m-approximation truthful mechanism is given in Lehmann, O’Callaghan, & Shoham for the case of single minded bidders. We narrow the gap between... |