## Auctions with budget constraints (2004)

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Venue: | In 9th Scandinavian Workshop on Algorithm Theory (SWAT |

Citations: | 27 - 1 self |

### BibTeX

@INPROCEEDINGS{Andelman04auctionswith,

author = {Nir Andelman and Yishay Mansour},

title = {Auctions with budget constraints},

booktitle = {In 9th Scandinavian Workshop on Algorithm Theory (SWAT},

year = {2004},

pages = {26--38}

}

### Years of Citing Articles

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### Abstract

Abstract. In a combinatorial auction k different items are sold to n bidders, where the objective of the seller is to maximize the revenue. The main difficulty to find an optimal allocation is due to the fact that the valuation function of each bidder for bundles of items is not necessarily an additive function over the items. An auction with budget constraints is a common special case where bidders generally have additive valuations, yet they have a limit on their maximal valuation. Auctions with budget constraints were analyzed by Lehmann, Lehmann and Nisan [11], as part of a wider class of auctions, where they have shown that maximizing the revenue is NP-hard, and presented a greedy 2-approximation algorithm. In this paper we present exact and approximate algorithms for auctions with budget constraints. We present a randomized algorithm with an e approximation ratio of ≈ 1.582, which can be derandomized. We e−1 analyze the special case where all bidders have the same budget constraint, and show an algorithm whose approximation ratio is between 1.3837 and 1.3951. We also present an FPTAS for the case of a constant number of bidders. 1

### Citations

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Reducibility among combinatorial problems
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(Show Context)
Citation Context ...nding an optimal allocation is NP-hard even if there are only two bidders with additive valuations up to budget constraints. The following theorem (the proof is based on a reduction from P ART IT ION =-=[9]-=-), strengthens this result. Theorem 1. Finding the optimal allocation for an auction with budget constraints is NP-hard even for two bidders with identical bids and budget constraints. (1)sUsing dynam... |

712 | Introduction to Algorithms, second edition
- Cormen, Leiserson, et al.
- 2001
(Show Context)
Citation Context ...this result. Theorem 1. Finding the optimal allocation for an auction with budget constraints is NP-hard even for two bidders with identical bids and budget constraints. (1)sUsing dynamic programming =-=[3]-=-, an exact solution can be found in a time complexity that is exponential in the number of items. In the i-th stage of the dynamic programming, optimal allocations of any subset of the k items are com... |

515 | Algorithm for optimal winner determination in combinatorial auctions
- Sandholm
- 2002
(Show Context)
Citation Context ... this difficulty, such as finding an approximate allocation rather than the optimal one [11, 6] or developing mechanisms which work well in practice, though do not necessarily have a formal guarantee =-=[6, 10, 14, 16]-=-. Lehmann, Lehmann and Nisan [11] have concentrated on combinatorial auctions where bidders’ valuations are known to be subadditive. A very natural subclass of subadditive valuations is decreasing mar... |

313 | Computationally manageable combinatorial auctions
- Rothkopf, Pekeč, et al.
- 1998
(Show Context)
Citation Context ...the economic efficiency. Finding an optimal allocation ⋆ Partially supported by a grant of the Israeli Science Foundationsis computationally hard in general, although it is tractable in certain cases =-=[14, 15, 17]-=-. There are various methods to tackle this difficulty, such as finding an approximate allocation rather than the optimal one [11, 6] or developing mechanisms which work well in practice, though do not... |

268 | Taming the Computational Complexity of Combinatorial Auctions: Optimal and Approximate Approaches
- Fujishima, Leyton-Brown, et al.
- 1999
(Show Context)
Citation Context ...lly hard in general, although it is tractable in certain cases [14, 15, 17]. There are various methods to tackle this difficulty, such as finding an approximate allocation rather than the optimal one =-=[11, 6]-=- or developing mechanisms which work well in practice, though do not necessarily have a formal guarantee [6, 10, 14, 16]. Lehmann, Lehmann and Nisan [11] have concentrated on combinatorial auctions wh... |

244 | Bidding and Allocation in Combinatorial Auctions
- Nisan
(Show Context)
Citation Context ...the economic efficiency. Finding an optimal allocation ⋆ Partially supported by a grant of the Israeli Science Foundationsis computationally hard in general, although it is tractable in certain cases =-=[14, 15, 17]-=-. There are various methods to tackle this difficulty, such as finding an approximate allocation rather than the optimal one [11, 6] or developing mechanisms which work well in practice, though do not... |

201 | Approximation algorithms for scheduling unrelated parallel machines - Lenstra, Shmoys, et al. - 1990 |

142 | 2006): “Combinatorial Auctions with Decreasing Marginal Utilities
- Lehmann, Lehmann, et al.
(Show Context)
Citation Context ... a common special case where bidders generally have additive valuations, yet they have a limit on their maximal valuation. Auctions with budget constraints were analyzed by Lehmann, Lehmann and Nisan =-=[11]-=-, as part of a wider class of auctions, where they have shown that maximizing the revenue is NP-hard, and presented a greedy 2-approximation algorithm. In this paper we present exact and approximate a... |

105 | An approximate truthful mechanism for combinatorial auctions with singleparameter agents
- Archer, Papadimitriou, et al.
- 2003
(Show Context)
Citation Context ...y. Designing truthful mechanisms that use approximate allocations is a challengingstask, and was successfully accomplished under certain assumptions on the bidders’ valuations and the auctioned items =-=[1, 2, 4, 5, 7, 13]-=-. In contrast, we concentrate only on maximizing the auctioneer’s revenue given the bids of the bidders. This approach is reasonable if the bidders are indifferent to the allocation mechanism, as long... |

95 | Truthful approximation mechanisms for restricted combinatorial auctions: extended abstract
- MU’ALEM, NISAN
(Show Context)
Citation Context ...y. Designing truthful mechanisms that use approximate allocations is a challengingstask, and was successfully accomplished under certain assumptions on the bidders’ valuations and the auctioned items =-=[1, 2, 4, 5, 7, 13]-=-. In contrast, we concentrate only on maximizing the auctioneer’s revenue given the bids of the bidders. This approach is reasonable if the bidders are indifferent to the allocation mechanism, as long... |

90 | Incentive compatible multi unit combinatorial auctions
- Bartal, Gonen, et al.
- 2003
(Show Context)
Citation Context ...y. Designing truthful mechanisms that use approximate allocations is a challengingstask, and was successfully accomplished under certain assumptions on the bidders’ valuations and the auctioned items =-=[1, 2, 4, 5, 7, 13]-=-. In contrast, we concentrate only on maximizing the auctioneer’s revenue given the bids of the bidders. This approach is reasonable if the bidders are indifferent to the allocation mechanism, as long... |

87 | Competitive generalized auctions
- Fiat, Goldberg, et al.
- 2002
(Show Context)
Citation Context |

82 |
Exact and approximate algorithms for scheduling nonidentical processors
- Horowitz, Sahni
- 1976
(Show Context)
Citation Context ...ocation, and the running time is polynomial in the number of items k and in 1 . (The algorithm is an adaptation of the FPTAS for the scheduling ɛ problem with unrelated machines of Horowitz and Sahni =-=[8]-=-.) The algorithm uses sets of tuples (v1, a1, v2, a2, . . . , vn, an, t) to construct the approximation. Each tuple represents an allocation of a subsets of items to the users. Let vi be the benefit o... |

24 | Truthful and competitive double auctions
- Deshmukh, Goldberg, et al.
(Show Context)
Citation Context |

21 | Competitiveness via consensus
- Goldberg, Hartline
(Show Context)
Citation Context |

13 | Bidding clubs in first-price auctions
- Leyton-Brown, Shoham, et al.
- 2002
(Show Context)
Citation Context ... this difficulty, such as finding an approximate allocation rather than the optimal one [11, 6] or developing mechanisms which work well in practice, though do not necessarily have a formal guarantee =-=[6, 10, 14, 16]-=-. Lehmann, Lehmann and Nisan [11] have concentrated on combinatorial auctions where bidders’ valuations are known to be subadditive. A very natural subclass of subadditive valuations is decreasing mar... |

7 |
Tractable combinatorial auctions and b-matching
- Tennenholtz
- 2002
(Show Context)
Citation Context ...the economic efficiency. Finding an optimal allocation ⋆ Partially supported by a grant of the Israeli Science Foundationsis computationally hard in general, although it is tractable in certain cases =-=[14, 15, 17]-=-. There are various methods to tackle this difficulty, such as finding an approximate allocation rather than the optimal one [11, 6] or developing mechanisms which work well in practice, though do not... |