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## On Revenue Maximization with Sharp Multi-Unit Demands (2012)

Venue: | In CoRR, arXiv:arXiv:1210.0203 |

Citations: | 4 - 3 self |

### Citations

2391 |
Microeconomic Theory
- Mas-Colell, Whinston, et al.
- 1995
(Show Context)
Citation Context ...very unallocated item is priced at zero (i.e., market clearance). Competitive equilibrium is one of the central solution concepts in economics and has been studied and applied in a variety of domains =-=[24]-=-. Combining the considerations from the two sides of the market, an ideal solution concept therefore would be revenue maximizing competitive equilibrium. For sharp multi-unit demand buyers, when the v... |

552 | Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords, American Economic Review, forthcoming
- Edelman, Ostrovsky, et al.
- 2007
(Show Context)
Citation Context ...) and a value vi (the benefit to i for an item of unit quality). Thus, the valuation that i obtains from item j is given by vij = viqj . The viqj valuation model has been considered by Edelman et al. =-=[13]-=- and Varian [28] in their seminal work for keywords advertising. We will focus on the sharp demand case, where every buyer requests exactly di items. This scenario captures some similarity but is stil... |

323 | Position auctions
- Varian
- 2006
(Show Context)
Citation Context ... (the benefit to i for an item of unit quality). Thus, the valuation that i obtains from item j is given by vij = viqj . The viqj valuation model has been considered by Edelman et al. [13] and Varian =-=[28]-=- in their seminal work for keywords advertising. We will focus on the sharp demand case, where every buyer requests exactly di items. This scenario captures some similarity but is still quite differen... |

304 |
The assignment game I: the core
- Shapley, Shubik
- 1972
(Show Context)
Citation Context ...ate solution concepts to be applicable in the domains where the valuations are correlated with respect to the quality of the items. Competitive equilibrium Envy-free pricing Unit demand existence yes =-=[27]-=- yes (trivial) (general values vij) max revenue computation P [27, 11] NP-hard [21] not always (P decidable) Sharp multi-unit demand existence (NP-hard for general vij) yes (trivial) (vij = viqj) max ... |

205 |
Multi-item auctions.
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- 1986
(Show Context)
Citation Context ...luations are correlated with respect to the quality of the items. Competitive equilibrium Envy-free pricing Unit demand existence yes [27] yes (trivial) (general values vij) max revenue computation P =-=[27, 11]-=- NP-hard [21] not always (P decidable) Sharp multi-unit demand existence (NP-hard for general vij) yes (trivial) (vij = viqj) max revenue P (constant demand) computation P (if one exists) NP-hard (arb... |

161 |
Walrasian equilibrium with gross substitutes.
- Gul, Stachetti
- 1999
(Show Context)
Citation Context ...rs have relaxed multi-unit demand (i.e., one can buy a subset of at most di items), where it is well known that the set of competitive equilibrium prices is non-empty and forms a distributive lattice =-=[27, 20]-=-. This immediately implies the existence of an equilibrium with maximum possible prices; hence, revenue is maximized. Demange, Gale, and Sotomayor [11] proposed a combinatorial dynamics which always c... |

122 | On profit-maximizing envy-free pricing,”
- Guruswami, Hartline, et al.
- 2005
(Show Context)
Citation Context ...vy-free pricing is a natural solution concept that can be applied in those marketplaces. The study of algorithmic computation of revenue maximizing envy-free pricing was initiated by Guruswami et al. =-=[21]-=-, where the authors considered two special settings with unit demand buyers and single-minded buyers and showed that a revenue maximizing envy-free pricing is NP-hard to compute. Because envy-free pri... |

95 |
Multi-Unit Auctions with Uniform Prices”, Economic Theory
- Engelbrecht-Wiggans, Kahn
- 1998
(Show Context)
Citation Context ...ndidate winner set is fixed. Both the linear programming and the dynamic programming run in polynomial time. 1.1 Related Work There are extensive studies on multi-unit demand in economics, see, e.g., =-=[1, 15, 7]-=-. Our study focuses on sharp demand buyers. An alternative model is when buyers have relaxed multi-unit demand (i.e., one can buy a subset of at most di items), where it is well known that the set of ... |

76 | Approximation algorithms and online mechanisms for item pricing,”
- Balcan, Blum
- 2006
(Show Context)
Citation Context ...y, there is a surge of studies on its computational issues since the pioneering work of [21], mainly focusing on approximation solutions and special cases that admit polynomial time algorithms, e.g., =-=[22, 2, 6, 3, 5, 9, 17, 14, 8, 19]-=-. The NP-hardness result of [21] for unit demand buyers implies that we cannot hope for a polynomial time algorithm for general vij valuations in the multi-unit demand setting, even for the very speci... |

41 | Item pricing for revenue maximization,”
- Balcan, Blum, et al.
- 2008
(Show Context)
Citation Context ...y, there is a surge of studies on its computational issues since the pioneering work of [21], mainly focusing on approximation solutions and special cases that admit polynomial time algorithms, e.g., =-=[22, 2, 6, 3, 5, 9, 17, 14, 8, 19]-=-. The NP-hardness result of [21] for unit demand buyers implies that we cannot hope for a polynomial time algorithm for general vij valuations in the multi-unit demand setting, even for the very speci... |

31 | Uniform Budgets and the Envy-Free Pricing Problem
- Briest
- 2008
(Show Context)
Citation Context ...y, there is a surge of studies on its computational issues since the pioneering work of [21], mainly focusing on approximation solutions and special cases that admit polynomial time algorithms, e.g., =-=[22, 2, 6, 3, 5, 9, 17, 14, 8, 19]-=-. The NP-hardness result of [21] for unit demand buyers implies that we cannot hope for a polynomial time algorithm for general vij valuations in the multi-unit demand setting, even for the very speci... |

27 | Computing optimal bundles for sponsored search
- Ghosh, Nazerzadeh, et al.
- 2007
(Show Context)
Citation Context ...ation) [4, 26] that would usually need a fixed number of positions while text ads would need only one position each. It has been formulated as a sharp-demand model in sponsored search in recent works =-=[18, 12]-=-. We study the economic problem as a two-sided market where the supply side is composed of m indivisible items and each item j has a parameter qj , measuring the quality of the item. For example, in T... |

20 | Approximation algorithms for single-minded envyfree profit-maximization problems with limited supply, to appear, FOCS
- Cheung, Swamy
- 2008
(Show Context)
Citation Context ...chanism for envy-free pricing problem [16]. Their model is special case of our model with all qualities equalling to 1. Another stream of research is on single-minded bidders, including, for example, =-=[21, 3, 2, 6, 10, 14]-=-. To the best of our knowledge, this paper is the first to study algorithmic computation of sharp multi-unit demand. 2 Preliminaries We have a market with m indivisible items, M = {1, 2, . . . ,m}, wh... |

18 | Optimal envy-free pricing with metric substitutability
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- 2008
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Citation Context |

17 |
Google’s auction for tv ads
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- 2009
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Citation Context ...publisher faces is how to allocate the items to customers at which prices. Demand is a practical consideration and has occurred in a number of applications. For instance, in TV (or radio) advertising =-=[25]-=-, advertisers may request different lengths of advertising slots for their ads programs. In banner (or newspaper) advertising, advertisers may request different sizes or areas for their displayed ads,... |

12 | Pricing on paths: A ptas for the highway problem
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- 2011
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Citation Context |

10 | On profit-maximizing pricing for the highway and tollbooth problems
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Citation Context |

8 |
The creativeness & effectiveness of online interactive rich media advertising.
- Rosenkrans
- 2009
(Show Context)
Citation Context ... ads, which may be decomposed into a number of base units. A remarkable application of our model is where advertisers choose to display their advertisement using rich medias (video, audio, animation) =-=[4, 26]-=- that would usually need a fixed number of positions while text ads would need only one position each. It has been formulated as a sharp-demand model in sponsored search in recent works [18, 12]. We s... |

5 |
Revenue maximizing envy-free multi-unit auctions with budgets
- Feldman, Fiat, et al.
- 2012
(Show Context)
Citation Context ...reak. Therefore, the market clearance condition becomes arguably unnecessary in those applications. This motivates the study of envy-free pricing(here envy-free pricing we mean envy-free item pricing =-=[16]-=-) which only requires the fairness condition in the competitive equilibrium, where no buyer can get a larger utility from any other allocation for the given prices. In contrast with competitive equili... |

3 |
Combination Bidding in Multi-Unit Auctions’, CEPR Discussion Papers,
- Cantillon, Pesendorfer
- 2007
(Show Context)
Citation Context ...ndidate winner set is fixed. Both the linear programming and the dynamic programming run in polynomial time. 1.1 Related Work There are extensive studies on multi-unit demand in economics, see, e.g., =-=[1, 15, 7]-=-. Our study focuses on sharp demand buyers. An alternative model is when buyers have relaxed multi-unit demand (i.e., one can buy a subset of at most di items), where it is well known that the set of ... |

2 |
Demand Revelation and Inefficiency
- Ausubel, Cramton
- 1996
(Show Context)
Citation Context ...ndidate winner set is fixed. Both the linear programming and the dynamic programming run in polynomial time. 1.1 Related Work There are extensive studies on multi-unit demand in economics, see, e.g., =-=[1, 15, 7]-=-. Our study focuses on sharp demand buyers. An alternative model is when buyers have relaxed multi-unit demand (i.e., one can buy a subset of at most di items), where it is well known that the set of ... |

1 |
New Media Interative Advertising vs
- Bezjian-Avery, Calder, et al.
- 1998
(Show Context)
Citation Context ... ads, which may be decomposed into a number of base units. A remarkable application of our model is where advertisers choose to display their advertisement using rich medias (video, audio, animation) =-=[4, 26]-=- that would usually need a fixed number of positions while text ads would need only one position each. It has been formulated as a sharp-demand model in sponsored search in recent works [18, 12]. We s... |

1 |
Ming Yin, Yunhong Zhou, Mechanism Design for Multi-slot Ads Auction in Sponsored Search Markets
- Deng, Sun
(Show Context)
Citation Context ...ation) [4, 26] that would usually need a fixed number of positions while text ads would need only one position each. It has been formulated as a sharp-demand model in sponsored search in recent works =-=[18, 12]-=-. We study the economic problem as a two-sided market where the supply side is composed of m indivisible items and each item j has a parameter qj , measuring the quality of the item. For example, in T... |