### Citations

690 | Efficient mechanism for bilateral trading - Myerson, Satterthwaite - 1983 |

551 | Internet advertising and the generalized second price auction: Selling billions of dollars worth of keywords
- Edelman, Ostrovsky, et al.
- 2006
(Show Context)
Citation Context ... important industry. The search engine based advertising model, the sponsored search auction, has been extensively studied in the literatures since the pioneer work of Edelman, Ostrovsky, and Schwarz =-=[28]-=-, as well as Varian [57], in the context of position auction, especially on the generalized second price auction (GSP). Here each position for placing an ad is associated with a quality value represen... |

328 | Platform Competition in Two-Sided Markets.”
- Rochet, Tirole
- 2003
(Show Context)
Citation Context ...er and a group of sellers. They gave several constant approximate mechanism with various buyer behaviour assumptions. While our setting assumes the existence of a monopoly platform, Rochet and Tirole =-=[54]-=- and Armstrong [2] introduced several different models for two-sided markets and studied platform competition.Chapter 2 Preliminaries In our model, a banner advertisement instance consists of n adver... |

322 | Position auctions
- Varian
- 2007
(Show Context)
Citation Context ... search engine based advertising model, the sponsored search auction, has been extensively studied in the literatures since the pioneer work of Edelman, Ostrovsky, and Schwarz [28], as well as Varian =-=[57]-=-, in the context of position auction, especially on the generalized second price auction (GSP). Here each position for placing an ad is associated with a quality value representing the prominence of t... |

301 |
The assignment game I: The core
- Shapley, Shubik
- 1972
(Show Context)
Citation Context ...our study for relaxed demand model shares the similar property of unit demand model where it is well known that the set of competitive equilibrium prices is non-empty and forms a distributive lattice =-=[38, 55]-=-. This immediately implies the existence of an equilibrium with maximum possible prices; hence, revenue is maximized. Demange, Gale, and Sotomayor [21] proposed a combinatorial dynamics which always c... |

205 |
Multi-item auctions.
- Demange, Gale, et al.
- 1986
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Citation Context ...s non-empty and forms a distributive lattice [38, 55]. This immediately implies the existence of an equilibrium with maximum possible prices; hence, revenue is maximized. Demange, Gale, and Sotomayor =-=[21]-=- proposed a combinatorial dynamics which always converges to a revenue maximizing (or minimizing) equilibrium for unit demand. However, Our study on sharp/consecutive demand buyers exhibit different s... |

161 |
Walrasian equilibrium with gross substitutes.
- Gul, Stachetti
- 1999
(Show Context)
Citation Context ...our study for relaxed demand model shares the similar property of unit demand model where it is well known that the set of competitive equilibrium prices is non-empty and forms a distributive lattice =-=[38, 55]-=-. This immediately implies the existence of an equilibrium with maximum possible prices; hence, revenue is maximized. Demange, Gale, and Sotomayor [21] proposed a combinatorial dynamics which always c... |

134 |
Complexity results for multiprocessor scheduling under resource constraints
- Garey, Johnson
- 1975
(Show Context)
Citation Context ...e integers, can S be partitioned into n subsets S1, . . . , Sn such that the sum of the numbers in each subset is equal? The 3 partition problem has been proven to be NP-complete in a strong sense in =-=[36]-=-, meaning that it remains NP-complete even when the integers in S are bounded above by a polynomial in n. Given a instance of 3 partition (a1, a2, . . . , a3n), we construct a instance for advertising... |

122 | On Profit-Maximizing Envy-free Pricing
- Guruswami, Hartline, et al.
- 2005
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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. =-=[39]-=-, 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 ...et constraints and demand constraints, 2-approximate mechanisms [1] and 4-approximate mechanisms [6] exist in the literature. There are extensive studies on multi-unit demand in economics, see, e.g., =-=[3, 12, 30]-=-. While our study for relaxed demand model shares the similar property of unit demand model where it is well known that the set of competitive equilibrium prices is non-empty and forms a distributive ... |

92 | An analysis of alternative slot auction designs for sponsored search
- Lahaie
- 2006
(Show Context)
Citation Context ...eoretical study of position auction (of 1 slot) under the generalized second price auction was initiated in [28, 57]. There has been a series of studies of position auctions in deterministic settings =-=[45]-=-. Our consideration of position auctions in the Bayesian setting fits in the general one dimensional auction design framework. Our study considersChapter 1. Introduction 7 continuous distributions on... |

75 | 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 [39], mainly focusing on approximation solutions and special cases that admit polynomial time algorithms, e.g., =-=[4, 5, 8, 9, 14, 18, 29, 34, 37, 40]-=-. The NP-hardness result of [39] 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... |

72 |
The double auction market institution: A survey
- Friedman
- 1993
(Show Context)
Citation Context ...plicated compared to single side auction since the market maker acts as the middle man to bring buyers and sellers together. A guide to the literature in micro-economics on this topic can be found in =-=[35]-=-. The profit maximization problem for the single buyer/single seller setting has been studied by Myerson and Satterthwaite [52]. Our optimal double auction is a direct extension of their work and, to ... |

51 | Approximation algorithms for knapsack problems with cardinality constraints,
- Caprara, Kellerer, et al.
- 2000
(Show Context)
Citation Context ...er simplified as follows: αidi Maximize: s.t. n∑ iviyi i=1 n∑ iyi ≤ m, i=1 n∑ yi ≤ d, i=1 yi ∈ Z + , ∀i ∈ [n] (5.14) Since (5.14) is a special two dimensional knapsack, then there is a PTAS for (5.14)=-=[13]-=-. If d is a constant, a brute force method takes nd time to valuate all the yi’s and gives the optimal solution. Remark 5.22. If the demand is sharp demand (which means buyer i would buy exactly di it... |

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 [39], mainly focusing on approximation solutions and special cases that admit polynomial time algorithms, e.g., =-=[4, 5, 8, 9, 14, 18, 29, 34, 37, 40]-=-. The NP-hardness result of [39] 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... |

39 | Bayesian Combinatorial Auctions: Expanding Single Buyer Mechanisms to Many Buyers
- Alaei
- 2011
(Show Context)
Citation Context ...er settings and very recently they also give a general reduction from revenue to welfare maximization in [11]; for buyers with both budget constraints and demand constraints, 2-approximate mechanisms =-=[1]-=- and 4-approximate mechanisms [6] exist in the literature. There are extensive studies on multi-unit demand in economics, see, e.g., [3, 12, 30]. While our study for relaxed demand model shares the si... |

38 | An Algorithmic Characterization of Multi-Dimensional Mechanisms
- Cai, Daskalakis, et al.
- 2012
(Show Context)
Citation Context ...the Bayesian setting fits in the general one dimensional auction design framework. Our study considersChapter 1. Introduction 7 continuous distributions on buyers’ values. For discrete distribution, =-=[10]-=- presents an optimal mechanism for budget constrained buyers without demand constraints in multiparameter settings and very recently they also give a general reduction from revenue to welfare maximiza... |

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 [39], mainly focusing on approximation solutions and special cases that admit polynomial time algorithms, e.g., =-=[4, 5, 8, 9, 14, 18, 29, 34, 37, 40]-=-. The NP-hardness result of [39] 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 | Near-Optimal Pricing in NearLinear Time - Hartline, Koltun - 2005 |

28 | Truthful and Competitive Double Auctions
- Deshmukh, Goldberg, et al.
- 2002
(Show Context)
Citation Context ...Myerson and Satterthwaite [52]. Our optimal double auction is a direct extension of their work and, to our best knowledge, fills a clear gap in the economic theory of double auctions. Deshmukh et al. =-=[26]-=-, studied the revenue maximization problem for double auctions when the auctioneer has no prior knowledge about bids. Their prior-free model is essentially different from ours. More auction mechanism ... |

25 | Budget constrained auctions with heterogeneous items.
- BHATTACHARYA, GOEL, et al.
- 2010
(Show Context)
Citation Context ...y also give a general reduction from revenue to welfare maximization in [11]; for buyers with both budget constraints and demand constraints, 2-approximate mechanisms [1] and 4-approximate mechanisms =-=[6]-=- exist in the literature. There are extensive studies on multi-unit demand in economics, see, e.g., [3, 12, 30]. While our study for relaxed demand model shares the similar property of unit demand mod... |

21 | Expressive banner ad auctions and model-based online optimization for clearing.
- Boutilier, Parkes, et al.
- 2008
(Show Context)
Citation Context ..., 9, 19, 29, 39]. To the best of our knowledge, we are the first to study algorithmic computation of multi-unit demand. Several works in the literature also made an effort to model online advertising =-=[7, 31, 53]-=-. However their focus on the design of expressive auctions and clearing algorithms is substantially different from this work. In their work, the advertisers’ consecutive demand are not taken into cons... |

21 | Optimize-and-dispatch architecture for expressive ad auctions.
- Parkes, Sandholm
- 2005
(Show Context)
Citation Context ..., 9, 19, 29, 39]. To the best of our knowledge, we are the first to study algorithmic computation of multi-unit demand. Several works in the literature also made an effort to model online advertising =-=[7, 31, 53]-=-. However their focus on the design of expressive auctions and clearing algorithms is substantially different from this work. In their work, the advertisers’ consecutive demand are not taken into cons... |

20 | Competition in Two-Sided Markets.” rAnd - Armstrong - 2006 |

20 | Approximation algorithms for single-minded envyfree profit-maximization problems with limited supply, to appear, FOCS
- Cheung, Swamy
- 2008
(Show Context)
Citation Context ...em with budget but without demand constraints and present a 2-approximate mechanism for envy-free pricing problem [32]. Another stream of research is on single-minded bidders, including, for example, =-=[4, 5, 9, 19, 29, 39]-=-. To the best of our knowledge, we are the first to study algorithmic computation of multi-unit demand. Several works in the literature also made an effort to model online advertising [7, 31, 53]. How... |

18 | Optimal envy-free pricing with metric substitutability
- Chen, Ghosh, et al.
- 2008
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Citation Context |

17 | Combination bidding in multi-unit auctions
- Cantillon, Pesendorfer
- 2007
(Show Context)
Citation Context ...et constraints and demand constraints, 2-approximate mechanisms [1] and 4-approximate mechanisms [6] exist in the literature. There are extensive studies on multi-unit demand in economics, see, e.g., =-=[3, 12, 30]-=-. While our study for relaxed demand model shares the similar property of unit demand model where it is well known that the set of competitive equilibrium prices is non-empty and forms a distributive ... |

12 | Pricing on paths: A ptas for the highway problem
- Grandoni, Rothvoß
- 2011
(Show Context)
Citation Context |

11 | A combinatorial allocation mechanism with penalties for banner advertising
- Feige, Immorlica, et al.
- 2008
(Show Context)
Citation Context ..., 9, 19, 29, 39]. To the best of our knowledge, we are the first to study algorithmic computation of multi-unit demand. Several works in the literature also made an effort to model online advertising =-=[7, 31, 53]-=-. However their focus on the design of expressive auctions and clearing algorithms is substantially different from this work. In their work, the advertisers’ consecutive demand are not taken into cons... |

10 | On profit-maximizing pricing for the highway and tollbooth problems
- Elbassioni, Raman, et al.
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Citation Context |

9 | Envy-free allocations for budgeted bidders
- Kempe, Mu’alem, et al.
- 2009
(Show Context)
Citation Context ...estion 7.1.6. How to generalize the results on envy-freeness for unit demand model to the same setting with budget constraints (including generalization of hardness result)? The study of Kempe et al. =-=[44]-=- and Devanur et al. [27] can be viewed as a generalization to solve problem 7.1.6. Another streams of general valuations are competitive equilibria. Chen et al. [16] studies competitive equilibrium on... |

7 |
Demand revelation and inefficiency in multi-unit auctions
- Ausubel, Cramton
- 1996
(Show Context)
Citation Context ...et constraints and demand constraints, 2-approximate mechanisms [1] and 4-approximate mechanisms [6] exist in the literature. There are extensive studies on multi-unit demand in economics, see, e.g., =-=[3, 12, 30]-=-. While our study for relaxed demand model shares the similar property of unit demand model where it is well known that the set of competitive equilibrium prices is non-empty and forms a distributive ... |

5 | Envy-Free Pricing in Multi-item Markets
- Chen, Deng
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Citation Context |

5 | Competitive equilibria in matching markets with budgets,
- Chen, Deng, et al.
- 2010
(Show Context)
Citation Context ...result)? The study of Kempe et al. [44] and Devanur et al. [27] can be viewed as a generalization to solve problem 7.1.6. Another streams of general valuations are competitive equilibria. Chen et al. =-=[16]-=- studies competitive equilibrium on unit demand matching market with budget constraints (e.g. utility function has one discontinuity point) and consistent conditions for the utility function and propo... |

5 |
Revenue maximizing envy-free multi-unit auctions with budgets
- Feldman, Fiat, et al.
- 2012
(Show Context)
Citation Context ...condition becomes arguably unnecessary in those applications. This motivates the study of envy-free pricing (here envy-free pricing we mean relaxed or sharp or consecutive or bundle envy-free pricing =-=[32]-=-) which only requires the fairness condition in the competitive equilibrium, where no buyer can get a larger utility fromChapter 1. Introduction 5 any other allocation for the given prices. In contra... |

5 |
On an algorithm of G. Birkhoff concerning doubly stochastic matrices", Canad
- Johnson, Dulmage, et al.
- 1960
(Show Context)
Citation Context ...omized mechanism to a realized allocation, we need a randomized rounding procedure satisfying the demand constraints. Fortunately, such a procedure is explicit in the the Birkhoff-Von Neumann theorem =-=[42]-=-. Thus, the relaxed demand constraint can be rewritten as ∑ By j (xij) ≤ di for each buyer i. using the characterization of BIC and virtual surplus, we can transform the revenue optimization problem t... |

4 | On revenue maximization with sharp multi-unit demands
- Chen, Deng, et al.
- 2012
(Show Context)
Citation Context ...2 3.3, 3.4 and 3.7 has been published in the paper [23]; Chapter 3.5, 3.6, 4.5, 5.5 and 6 has been published in the paper [22]; Chapter 4.1, 4.2, 4.3, 4.4, 5.1, 5.2, 5.3 and 5.4 appeared in the paper =-=[17]-=-. xisAbstract We consider revenue maximization problem in banner advertisements under two fundamental concepts: Envy-freeness and truthfulness. Envy-freeness captures fairness requirement among buyers... |

4 |
Mechanism design for multi-slot ads auction in sponsored search markets.
- DENG, SUN, et al.
- 2010
(Show Context)
Citation Context ...rk, the advertisers’ consecutive demand are not taken into consideration. Deng et al., had a study on the problem for the VCG protocol, and various GSP type protocols, together with a simulated study =-=[25]-=-. However, it only works in the special case of the sponsored search model where the slots are usually ranked from top to bottom in a decreasing order of their quality scores.Chapter 1. Introduction ... |

4 |
Incentive-compatibility and the bargaining problem. Econometrica 47
- Myerson
- 1979
(Show Context)
Citation Context ...he design of truthful mechanisms, the point here is that the value vi of each buyer i is initially private information of that buyer. Truthful market design relies on the general revelation principle =-=[50]-=- to simplify the search for mechanisms withChapter 1. Introduction 4 desirable properties, such as one that brings in the maximum revenue. Therefore, it is natural for us to consider market mechanism... |

4 |
auction design
- “Optimal
- 1981
(Show Context)
Citation Context ...ment instances in the context of mechanism design. Mechanism design studies algorithmic procedures where the input data is not always objective but reported from selfish agents. Following the work of =-=[51]-=-, we consider this problem in a Bayesian setting where the seller has a prior knowledge about the buyers’ distribution of valuations. This has been shown to be a standard assumption if one wants to op... |

2 |
multi-dimensional mechanism design: Reducing revenue to welfare maximization
- “Optimal
- 2012
(Show Context)
Citation Context ...s an optimal mechanism for budget constrained buyers without demand constraints in multiparameter settings and very recently they also give a general reduction from revenue to welfare maximization in =-=[11]-=-; for buyers with both budget constraints and demand constraints, 2-approximate mechanisms [1] and 4-approximate mechanisms [6] exist in the literature. There are extensive studies on multi-unit deman... |

2 | Pricing Ad Slots with Consecutive Multi-unit Demand
- Deng, Goldberg, et al.
- 2013
(Show Context)
Citation Context ...chapters in this thesis have appeared in which paper as below. Chapter 3.1, 3.2 3.3, 3.4 and 3.7 has been published in the paper [23]; Chapter 3.5, 3.6, 4.5, 5.5 and 6 has been published in the paper =-=[22]-=-; Chapter 4.1, 4.2, 4.3, 4.4, 5.1, 5.2, 5.3 and 5.4 appeared in the paper [17]. xisAbstract We consider revenue maximization problem in banner advertisements under two fundamental concepts: Envy-freen... |

2 | Multi-unit Bayesian Auction with Demand or Budget Constraints
- Deng, Goldberg, et al.
- 2012
(Show Context)
Citation Context ...ofessional qualification except as specified. We illustrate that which chapters in this thesis have appeared in which paper as below. Chapter 3.1, 3.2 3.3, 3.4 and 3.7 has been published in the paper =-=[23]-=-; Chapter 3.5, 3.6, 4.5, 5.5 and 6 has been published in the paper [22]; Chapter 4.1, 4.2, 4.3, 4.4, 5.1, 5.2, 5.3 and 5.4 appeared in the paper [17]. xisAbstract We consider revenue maximization prob... |

2 |
Prior-free auctions for budgeted agents, arXiv preprint arXiv:1212.5766
- Devanur, Ha, et al.
- 2012
(Show Context)
Citation Context ...e envy-free benchmark from [41] to settings with budgets and characterize the optimal envy-free outcomes for both welfare and revenue, and give prior-free mechanisms that approximate these benchmarks =-=[27]-=-. For the multi-unit demand setting, Chen et al. [18] gave an O(log D) approximation algorithm when there is a metric space behind all items, where D is the maximum demand, and Briest [8] showed that ... |

1 |
Single-minded unlimited sup ply pricing on sparse instances
- Briest, Krysta
(Show Context)
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1 |
truthful market clearing bundle pricing, Internet and Network Economics
- Cohen, Feldman, et al.
- 2011
(Show Context)
Citation Context ...per bound on the demand of any single buyer X3C The exact cover by 3-sets problem GSP Generalized Second Prize Vk The kth sample vector {v1 k , v2 k , · · · , vn k }, where each vi k is sampled from U=-=[20, 80]-=-. viiiDefinitions The following definitions and concepts are found in this thesis: Bayesian Incentive Compatible Definition 2.1.1 Individual Rationality Definition 2.1 Relaxed Envy-free Pricing Defin... |

1 |
Mechanisms and impossibilities for truthful, envy-free allocations, Algorithmic Game Theory
- Feldman, Lai
- 2012
(Show Context)
Citation Context ... it might produce the price discrimination phenomenon that causes discontent among users and lures the arbitrage behavior. If we insist on truthful markets, the unfair auction is the only possibility =-=[20, 33]-=-. Market equilibrium (Competitive equilibrium) offers an alternative which offers a sense of fairness to all customers in terms of that no one would prefer to shift to another allocation under the cur... |

1 |
Envy, multi envy, and revenue maximization, Internet and Network Economics
- Fiat, Wingarten
- 2009
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1 |
ebay’s market intermediation problem
- Kamal, Christopher
- 2012
(Show Context)
Citation Context ...blems were studied by many researchers in recent years, but as far as we know, not in the context of optimal double auction design in the Bayesian setting. The most related one is by Jain and Wilkens =-=[43]-=-, where they studied the market intermediation problem in a setting with a single unit-demand buyer and a group of sellers. They gave several constant approximate mechanism with various buyer behaviou... |

1 |
Pricing display ads and contextual ads: Competition, acquisition
- Li, Jhang-Li
- 2009
(Show Context)
Citation Context ... 5. The simulation is presented in Section 6. 1.3 Related Works This thesis merges three work [17, 23? ]. A study on search based text ads and display based multi-media ads was conducted by Li and Li =-=[46]-=- to explore their profitabilities. Hunter discussed experimental results identifying factors that affect the prices of banner ads [56], for three types of ad size: 1 slot (mini), 2 slots (standard) an... |

1 |
Pricing banner advertisements in a social network of political weblogs
- Starling
(Show Context)
Citation Context ... ads and display based multi-media ads was conducted by Li and Li [46] to explore their profitabilities. Hunter discussed experimental results identifying factors that affect the prices of banner ads =-=[56]-=-, for three types of ad size: 1 slot (mini), 2 slots (standard) and 6 lots (hi-rise). The theoretical study of position auction (of 1 slot) under the generalized second price auction was initiated in ... |