## Iterative Combinatorial Auctions: Theory and Practice (2000)

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Citations: | 178 - 24 self |

### BibTeX

@MISC{Parkes00iterativecombinatorial,

author = {David C. Parkes and Lyle H. Ungar},

title = {Iterative Combinatorial Auctions: Theory and Practice},

year = {2000}

}

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### Abstract

Combinatorial auctions, which allow agents to bid directly for bundles of resources, are necessary for optimal auction-based solutions to resource allocation problems with agents that have non-additive values for resources, such as distributed scheduling and task assignment problems. We introduce iBundle, the first iterative combinatorial auction that is optimal for a reasonable agent bidding strategy, in this case myopic best-response bidding. Its optimality is proved with a novel connection to primal-dual optimization theory. We demonstrate orders of magnitude performance improvements over the only other known optimal combinatorial auction, the Generalized Vickrey Auction.

### Citations

1276 |
Combinatorial Optimization. Algorithms and Complexity
- Papadimitriou, Steiglitz
- 1998
(Show Context)
Citation Context ...gy, in this case myopic utility-maximizing agents that place best-response bids to prices. In this paper we prove the optimality of iBundle with a novel connection to primal-dual optimization theory (=-=Papadimitriou & Steiglitz 1982-=-) that also suggests a useful methodology for the design and analysis of iterative auctions for other problems. iBundle has many computational advantages over the only other known optimal combinatoria... |

515 | Algorithm for Optimal Winner Determination in Combinatorial Auctions
- Sandholm
(Show Context)
Citation Context ...elect bundles of size 10 in Uniform. Results are presented for iBundle(2), the auction variation without price discrimination. A variation on Sandholm's depth-first branch-and-bound search algorithm (=-=Sandholm 1999-=-) solves winner-determination (WD) in each round, and computes the allocation and prices in the GVA. We introduce a new heuristic to make search more efficient for XOR bids. The heuristic computes an ... |

313 | Computationally manageable combinatorial auctions
- Rothkopf, Pekeč, et al.
- 1998
(Show Context)
Citation Context ...ism execution. In particular, the auctioneer's winner-determination (WD) problem, the problem of choosing bids to maximize revenue, is NP - hard by reduction from the maximal weighted clique problem (=-=Rothkopf et al. 1998-=-). In iBundle the auctioneer must solve a sequence of WD problems (one in each round) to maintain a provisional allocation as agents bid. In comparison, in the GVA the auctioneer must solve one WD pro... |

274 | A market-oriented programming environment and its application to distributed multicommodity flow problems
- Wellman
- 1993
(Show Context)
Citation Context ...ents. Typical applications include task assignment and distributed scheduling problems, and are characterized with distributed information about agents' local problems and multiple conflicting goals (=-=Wellman 1993-=-; Clearwater 1996). Auctions can minimize communication within a system, and generate optimal (or near-optimal) solutions that maximize the sum value over all agents. More recently, electronic commerc... |

264 |
An implementation of the contract net protocol based on marginal cost calculations
- Sandholm
- 1993
(Show Context)
Citation Context ...dles for which it has positive value. This is often impossible, since for jGj items there are 2 jGj bundles to value, each of which may require solving a difficult optimization problem (Parkes 1999a; =-=Sandholm 1993-=-). However, combinatorial auctions introduce new computational complexities in mechanism execution. In particular, the auctioneer's winner-determination (WD) problem, the problem of choosing bids to m... |

110 | i-bundle: An efficient ascending price bundle auction
- Parkes
- 1999
(Show Context)
Citation Context ...ue of, all bundles for which it has positive value. This is often impossible, since for jGj items there are 2 jGj bundles to value, each of which may require solving a difficult optimization problem (=-=Parkes 1999-=-a; Sandholm 1993). However, combinatorial auctions introduce new computational complexities in mechanism execution. In particular, the auctioneer's winner-determination (WD) problem, the problem of ch... |

109 | The FCC Spectrum Auctions: An Early Assessment
- Cramton
- 1997
(Show Context)
Citation Context ...e, in the FCC broadband spectrum auction, conducted as a set of simultaneous ascending-price auctions on spectrum licenses, bids were rarely above minimum ask prices and jump bids were the exception (=-=Cramton 1997-=-). In Parkes & Ungar (2000) we present a simple extension to iBundle that makes it robust to strategic manipulation in several interesting problems; we adjust the final prices in iBundle towards Vickr... |

107 | Allocating uncertain and unresponsive resources: An experimental approach - Banks, Ledyard, et al. - 1989 |

97 | A new and improved design for multiobject iterative auctions. Management Sci - Kwasnica, Ledyard, et al. - 2005 |

87 |
The package assignment model
- Bikhchandani, Ostroy
- 2006
(Show Context)
Citation Context ...well in many hard problems, achieving an average of 99% allocative ef4 Label 2 refers to "second-degree" price discrimination, nonlinear prices in bundles of items but identical prices acros=-=s agents (Bikchandani & Ostroy 1998-=-). ficiency 5 (Parkes 1999b) compared to 82% allocative efficiency from non-combinatorial auctions in the same problems. We found that price discrimination only had a noticeable effect on allocative e... |

75 | Truth revelation in rapid, approximately efficient combinatorial auctions
- Lehmann, O’Callaghan, et al.
(Show Context)
Citation Context ...tions while maintaining incentives for truth-revelation; e.g. limit the types of bundles that agents can bid for (Rothkopf et al. 1998); or introduce an approximate solution for winner-determination (=-=Lehmann et al. 1999-=-), but little success in designing good auctions for general bundle problems. Moreover, most previous work focuses on sealed-bid auctions. Conclusions iBundle is a new iterative combinatorial auction ... |

62 | Optimal auction design for agents with hard valuation problems
- Parkes
- 1999
(Show Context)
Citation Context ...ue of, all bundles for which it has positive value. This is often impossible, since for jGj items there are 2 jGj bundles to value, each of which may require solving a difficult optimization problem (=-=Parkes 1999-=-a; Sandholm 1993). However, combinatorial auctions introduce new computational complexities in mechanism execution. In particular, the auctioneer's winner-determination (WD) problem, the problem of ch... |

62 | Generalized Vickrey auctions
- MacKie-Mason, Varian
- 1994
(Show Context)
Citation Context ...design and analysis of iterative auctions for other problems. iBundle has many computational advantages over the only other known optimal combinatorial auction, the Generalized Vickrey Auction (GVA) (=-=Varian & MacKie-Mason 1995-=-). As an iterative auction, agents can incrementally compute values for different bundles of items as prices change, and make new bids in response to bids from other agents. In comparison, the GVA is ... |

59 | Preventing strategic manipulation in iterative auctions: Proxy agents and price-adjustment - Parkes, Ungar - 2000 |

54 | Mutually destructive bidding: The FCC auction design problem - Bykowsky, Cull, et al. - 2000 |

43 |
The auction algorithm for assignment and other network flow problems: A tutorial,” Interfaces
- Bertsekas
- 1990
(Show Context)
Citation Context ...arge enough cache is constructed, and solving WD when an auction is about to terminate with cached solutions. Another useful approach is ffl-scaling, that adjusts the bid increment during an auction (=-=Bertsekas 1990-=-). Related Work Rassenti et al. (1982) describe an early single-round combinatorial mechanism for airport slot allocation, while Banks et al. (1989) describe AUSM, an early iterative bundle auction.sA... |

25 | A combinatorial mechanism for airport time slot allocation - Smith, Bulfin - 1982 |

4 |
Integer programming for auctions with bids for combinations
- Andersson, Tenhunen, et al.
- 2000
(Show Context)
Citation Context ...in the previous round. Moreover, although each intermediate WD problem in iBundle may be intrinsically more difficult than each WD problem in GVA because all agents bid at similar prices for bundles (=-=Andersson et al. 2000-=-), the problems are typically much smaller than in the GVA. The auctioneer only announces price increases in each round, and need not maintain explicit prices for all possible bundles. Bid prices are ... |