## Computing With Strategic Agents (2005)

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Citations: | 3 - 2 self |

### BibTeX

@TECHREPORT{Immorlica05computingwith,

author = {Nicole Immorlica and Erik D. Demaine},

title = {Computing With Strategic Agents},

institution = {},

year = {2005}

}

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### Abstract

This dissertation studies mechanism design for various combinatorial problems in the presence of strategic agents. A mechanism is an algorithm for allocating a resource among a group of participants, each of which has a privately-known value for any particular allocation. A mechanism is truthful if it is in each participant’s best interest to reveal his private information truthfully regardless of the strategies of the other participants. First, we explore a competitive auction framework for truthful mechanism design in the setting of multi-unit auctions, or auctions which sell multiple identical copies of a good. In this framework, the goal is to design a truthful auction whose revenue approximates that of an omniscient auction for any set of bids. We focus on two natural settings — the limited demand setting where bidders desire at most a fixed number of copies and the limited budget setting where bidders can spend at most a fixed amount of money. In the limit demand setting, all prior auctions employed the use of randomization in the computation of the allocation and prices. Randomization

### Citations

1279 |
Counterspeculation, auctions, and competitive sealed tenders
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(Show Context)
Citation Context ...sions which maximize the social welfare or the revenue. A prominent example of a truthful mechanism is the Vickrey-Clark-Groves mechanism, or VCG mechanism, developed in a series of papers by Vickrey =-=[115]-=-, Clark [19], and Groves [52] for a general setting where agents have quasi-linear utility functions. The VCG mechanism is a direct revelation auction that chooses a decision that maximizes the social... |

1115 |
Theory of Games and Economic Behavior
- Neumann
- 1944
(Show Context)
Citation Context ...alitional game with transferable payoff, where the cost function is replaced by a function that gives the value, or the worth of each set. This notion was first defined by von Neumann and Morgenstern =-=[116]-=-. 103sIntuitively, we think of ξ(i, S) as the share of i in the total cost if S is the set of agents receiving the service. Ideally, we want cost sharing schemes (and cost allocations) to be budget-ba... |

1017 | Optimal Auction Design - Myerson |

836 |
The Theory of Learning in Games
- Fudenberg, Levine
- 1998
(Show Context)
Citation Context ...zumaj and Ronen [20] propose a mechanism which combines dominant 4 Substantial effort has been made to understand when we might expect mechanisms to exhibit these weaker equilibria (see, for example, =-=[38]-=-). 19sand non-dominant strategy mechanisms; however they show that it has an arbitrary ratio between the payment of different equilibria and say that overall, “finding a natural and tractable measure ... |

740 |
Multipart pricing of public goods
- Clarke
- 1971
(Show Context)
Citation Context ...aximize the social welfare or the revenue. A prominent example of a truthful mechanism is the Vickrey-Clark-Groves mechanism, or VCG mechanism, developed in a series of papers by Vickrey [115], Clark =-=[19]-=-, and Groves [52] for a general setting where agents have quasi-linear utility functions. The VCG mechanism is a direct revelation auction that chooses a decision that maximizes the social welfare, or... |

668 |
College admissions and the stability of marriage
- Gale, LS
- 1962
(Show Context)
Citation Context ...young lovers who prefer each other to their assigned spouses. Such a set of marriages is called stable, and finding a set of stable marriages is known as the stable marriage problem. Gale and Shapley =-=[39]-=- showed that the stable marriage problem always has a solution and developed an algorithm, called the deferred acceptance algorithm, to find it. Since the seminal work of Gale and Shapley, there has b... |

605 |
Incentives in teams
- Groves
- 1973
(Show Context)
Citation Context ...l welfare or the revenue. A prominent example of a truthful mechanism is the Vickrey-Clark-Groves mechanism, or VCG mechanism, developed in a series of papers by Vickrey [115], Clark [19], and Groves =-=[52]-=- for a general setting where agents have quasi-linear utility functions. The VCG mechanism is a direct revelation auction that chooses a decision that maximizes the social welfare, or the sum of value... |

580 |
Auction theory
- Krishna
- 2002
(Show Context)
Citation Context ...c offering of Google stock. Several auction formats have been proposed for these settings, the most abundant 23sbeing the discriminatory auction and the uniform-price auction (see the book by Krishna =-=[74]-=- for a survey on multi-unit auctions). A standard goal in the design of multi-unit auctions, and auction design in general, is to maximize revenue. One approach to maximizing revenue, traditionally ap... |

569 | Algorithmic mechanism design
- Nisan, Ronen
(Show Context)
Citation Context ...s in the system such that these equilibria result in globally optimal solutions. Algorithmic mechanism design focuses on the application of mechanism design to computationally intensive settings (see =-=[89]-=- for an introduction). 1.1 Mechanism Design We consider a setting in which there is a set N of n agents denoted {1, . . . , n} which must collectively reach a common decision from a set of feasible de... |

453 |
A value for n-person games
- Shapley
- 1953
(Show Context)
Citation Context ... constructing group-strategyproof mechanisms based on combinatorial constructions called cross-monotonic cost-sharing schemes. This results together with cost-sharing schemes such as those of Shapley =-=[107]-=- or Dutta and Ray [26] imply budget-balanced group-strategyproof mechanisms for any submodular cost function. However, many interesting cost functions based on combinatorial optimization problems are ... |

419 |
Principles of Mathematical Analysis
- Rudin
- 1964
(Show Context)
Citation Context ...tion of bidder i must not increase which means his thresholds p j i As the r j i must be non-increasing. and sj i are non-decreasing, they can be discontinuous in at most a countable number of points =-=[102]-=-. Let T denote the set of points greater than C at which all of the above functions are continuous. Notice that since the number of discontinuity points of each of these functions is countable, the se... |

406 |
Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis
- Roth, Sotomayor
(Show Context)
Citation Context ...ficant amount of work on the mathematical structure of stable marriages and related algorithmic questions. See, for example, the books by Knuth [69], Gusfield and Irving [53], or Roth and Sotomayoror =-=[101]-=-. The stable marriage problem has many promising applications in two-sided markets such as job markets [98], college admissions [98], sorority/fraternity rush [83], and assignment of graduating rabbis... |

322 | Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and lagrangian relaxation
- Jain, Vazirani
(Show Context)
Citation Context ...ny cross-monotonic cost-sharing scheme for the facility location game is at most 1/3-budget balanced. 7 This example also shows that the dual computed by the Jain-Vazirani facility location algorithm =-=[65]-=- can be a factor 3 away from the optimal dual. 114sProof. Consider the following instance of the facility location problem. There are k sets A1, . . . , Ak of m cities each, where m = ω(k) and k = ω(1... |

260 | Sharing the Cost of Multicast Transmissions
- Feigenbaum, Papadimitriou, et al.
- 2001
(Show Context)
Citation Context ...derived from these schemes are themselves budget-balanced. These schemes have been applied to derive group-strategyproof mechanisms for important submodular cost functions such as multicast on a tree =-=[36, 34, 33]-=-. Unfortunately, many classes of important cost functions arise from (often NP-hard) optimization problems and fail to be submodular. For example, the cost of providing the service for a set S of agen... |

245 |
The Stable Marriage Problem: Structure and Algorithms
- Gusfield, Irving
- 1989
(Show Context)
Citation Context ...hapley, there has been a significant amount of work on the mathematical structure of stable marriages and related algorithmic questions. See, for example, the books by Knuth [69], Gusfield and Irving =-=[53]-=-, or Roth and Sotomayoror [101]. The stable marriage problem has many promising applications in two-sided markets such as job markets [98], college admissions [98], sorority/fraternity rush [83], and ... |

242 |
Computers and Intractability
- JOHNSON
- 1979
(Show Context)
Citation Context ...s straightforward to compute. In particular, if the network is a general directed graph, it is NP-hard to compute such a path, since it reduces to the two disjoint paths problem, which is NP-complete =-=[41]-=-. However, there are many interesting classes of graphs for which it is possible to compute such a path Pe in polynomial time, including undirected graphs and directed acyclic or planar graphs [41]. W... |

231 | A BGP-based mechanism for lowest-cost routing
- Feigenbaum, Papadimitriou, et al.
(Show Context)
Citation Context ...alled a flow, capable of routing his demand between the source and the sink. Nisan and Ronen [89] proposed applying the VCG mechanism to path auctions; Hershberger and Suri [55] and Feigenbaum et al. =-=[35]-=- study methods to make this mechanism efficiently computable and practical in this setting. However, as observed by Archer and Tardos [6], the VCG mechanism (and, in fact, all min function mechanisms)... |

218 |
Acceptable Points in General Cooperative n-person Games
- Aumann
- 1959
(Show Context)
Citation Context ...stcost set are likely to each reduce their price. This leads us to explore the concept of strong ɛ-Nash equilibria. 3.2.3 Strong ɛ-Nash Equilibria Strong ɛ-Nash equilibria, first introduced by Aumann =-=[9]-=- and used by Young [119], require that there is no group of agents who can deviate in a way that improves the payoff of each member by at least ɛ. Definition 10 A strong ɛ-Nash equilibrium is a set of... |

217 | The Evolution of the Labor Market for Medical Interns and Residents: a Case Study in Game Theory
- Roth
- 1984
(Show Context)
Citation Context ...plications. One particular job market — the medical residency market — has been using a centralized stable marriage market system called the National Residency Matching Program (NRMP) since the 1950s =-=[96]-=-. To this day, most medical residences are formed through an updated version of this centralized market system redesigned in 1998 by Roth [97]. 1 It seems surprising that an algorithm like the one use... |

202 |
The probabilistic method, Wiley-Interscience Series in Discrete Mathematics and Optimization, A Wiley-Interscience Publication
- Alon, Spencer
- 1992
(Show Context)
Citation Context ...=1 g� Pr[Ei] i=1 = E[Yg] 1≤i<j≤g Pr[Ei ∧ Ej] − g� Pr[Ei] 2 − 2 � i=1 1≤i<j≤g Pr[Ei] · Pr[Ej] as required. ✷ Using the above three lemmas and the Chebyshev inequality (see the book by Alon and Spencer =-=[3]-=- for a discussion of this and related inequalities), we can easily conclude the statement of Lemma 5.3.1. Proof of Lemma 5.3.1. Let q be the probability that Yg < E[Yg]/2. By the Chebyshev inequality ... |

191 | Truthful mechanisms for one-parameter agents
- Archer, Tardos
- 2001
(Show Context)
Citation Context ...e bounds converge quite quickly. Mechanisms that are truthful in a randomized sense (that is, in expectation, or with high probability) have been a subject of research in theoretical computer science =-=[4, 5]-=-. These mechanisms seek to encourage truthfulness by introducing randomization into the mechanism. Our results are of a different flavor. We show that one can conclude statements regarding truthfulnes... |

177 | Combinatorial auctions: a survey
- Vries, Vohra
- 2003
(Show Context)
Citation Context ...auctions, that is an auction for multiple copies of a single good. This setting is an important special case of the multi-object (combinatorial) auction setting (for a discussion of this setting, see =-=[22]-=-). We consider the revenue maximization problem under various assumptions regarding the form of the bidders’ utility functions. In particular, we assume bidders either have limited demand (have utilit... |

175 | The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics
- Roth
- 2002
(Show Context)
Citation Context ...ee, for example, the books by Knuth [69], Gusfield and Irving [53], or Roth and Sotomayoror [101]. The stable marriage problem has many promising applications in two-sided markets such as job markets =-=[98]-=-, college admissions [98], sorority/fraternity rush [83], and assignment of graduating rabbis to their first congregation [12]. Since most applications of the stable marriage algorithm involve the par... |

161 | Strategyproof Sharing of Submodular Costs: Budget Balance versus Efficiency
- Moulin, Shenker
- 2001
(Show Context)
Citation Context ...ves (VCG) auction for a single item, for 1 This impossibility result can be avoided by imposing a compatibility condition on individual beliefs and using a Bayesian model [21]. See Moulin and Shenker =-=[87]-=- for a discussion of the tradeoff between budget-balance and efficiency in our setting. 99sexample, the two highest bidders can collude to bid just above the value of the thirdhighest bidder. With suc... |

145 | Combinatorial Optimization
- Schrijver
- 2003
(Show Context)
Citation Context ... the flow which sends k/(k + 1) units of flow along the flow paths determined by Fc(k + 1). Since Fb(k) is a lowest-price k-flow with respect to b ′ and using the integrality of optimal network flows =-=[104]-=-, we have Define edge sets Then equation 3.8 reduces to � � k b k + 1 ′ (Fc(k + 1)) − b ′ (Fb(k)) ≥ 0. (3.8) E+ = {e ∈ Fc(k + 1) − Fb(k)} Eo = {e ∈ Fc(k + 1) ∩ Fb(k)} E− = {e ∈ Fb(k) − Fc(k + 1)} � � ... |

139 |
The Economics of Matching: Stability and Incentives
- Roth
- 1982
(Show Context)
Citation Context ...about their preference lists. Ideally, in economic settings such as job markets, we 131swould like to design truthful mechanisms which always output a stable matching. Unfortunately, as shown by Roth =-=[95]-=-, there is no mechanism for the stable marriage problem in which truth-telling is a dominant strategy for both men and women [101]. Nonetheless, stable matching algorithms have had spectacular success... |

131 | Competitive auctions and digital goods
- Goldberg, Hartline, et al.
- 2001
(Show Context)
Citation Context ...h maximum expected revenue. However, assuming a probability distribution for the bidders’ valuations is often unsatisfactory. In an effort to avoid any such assumption, Goldberg, Hartline, and Wright =-=[50]-=- proposed a framework called competitive auctions for designing highrevenue auctions. This framework seeks to maximize the ratio between the revenue 17sof an auction to the revenue of an omniscient au... |

128 | The Simple Economics of Optimal Auctions
- Bulow, Roberts
(Show Context)
Citation Context ...ximizing revenue, traditionally applied in the limited supply and/or limited demand case, is to determine an optimal reserve price based on assumptions about the distribution of values of the bidders =-=[16, 88]-=-. The budget-constrained case has also been investigated using this approach in several recent papers [11, 17, 18, 30, 31, 76, 79, 120] often in the context of privatization of high-value public goods... |

128 |
Core and Equilibria of a Large Economy
- Hildenbrand
- 1974
(Show Context)
Citation Context ...ore of markets and conclude that, under certain conditions, the size of the core shrinks as the size of the market grows (see, for example, the seminal paper of Aumann [10] or the book by Hildenbrand =-=[56]-=-). The set of stable matchings is the core of the stable marriage game, but our market setting is quite different from that in the literature. In fact, in our setting, the core is often large even tho... |

125 |
Incentives and incomplete information
- d’Aspremont, Gérard-Varet
- 1979
(Show Context)
Citation Context ...ude. In the Vickrey-Clark-Groves (VCG) auction for a single item, for 1 This impossibility result can be avoided by imposing a compatibility condition on individual beliefs and using a Bayesian model =-=[21]-=-. See Moulin and Shenker [87] for a discussion of the tradeoff between budget-balance and efficiency in our setting. 99sexample, the two highest bidders can collude to bid just above the value of the ... |

124 |
An Exploration in the Theory of Optimal Income Taxation
- Mirrlees
- 1971
(Show Context)
Citation Context ...e following theorem which states that the price charged to a bidder must be independent of his bid. Statements similar to this one have appeared in numerous places and date back to at least the 1970s =-=[82]-=-. For simplicity, we state the characterization for the special case of a single-item auction in which each bidder’s utility is quasi-linear (see Proposition 2.3.1 for a generalization to a non-quasi-... |

119 | Mechanism theory
- Jackson
- 2002
(Show Context)
Citation Context ..., they believe will maximize their own gain. The field of mechanism design or implementation theory attempts to build systems taking into consideration the strategic behavior of the participants (see =-=[62, 63]-=- for a survey). The basic paradigm postulates that each individual maintains some private information relevant to the problem at hand. A system solicits from participants their private information and... |

116 | V.: Applications of approximation algorithms to cooperative games
- Jain, Vazirani
- 2001
(Show Context)
Citation Context ... for some problems can be perfectly budget-balanced. Accordingly, approximately budget-balanced schemes have been proposed for many combinatorial optimization problems including minimum spanning tree =-=[64, 68]-=-, Steiner tree [64], Steiner forest [72], facility location [90], and connected facility location [78]. In Chapter 4, we provide a general methodology to prove upper bounds on the fraction of cost rec... |

116 | Towards a Characterization of Truthful Combinatorial Auctions’, manuscript
- Lavi, Mu’alem, et al.
- 2003
(Show Context)
Citation Context ...mple sell at most one unit to each bidder. The second property, which we call the independence of irrelevant alternatives (IIA), is a much weaker version of a property of the same name in Lavi et al. =-=[77]-=-. This property is defined as follows. • independence of irrelevant alternatives (IIA) – For any agent i and a bid vector (u, b), if i receives no units at (u, b), then the allocation when every agent... |

112 |
On balanced sets and cores
- Shapley
- 1967
(Show Context)
Citation Context ...he best budget-balance factor achievable by a cross-monotonic cost sharing scheme cannot be better than that of a cost sharing in the core. A simple extension of the classic Bondareva-Shapley theorem =-=[13, 108]-=- implies that the best budget-balance factor for a cost sharing in the core of integer covering games is equal to the integrality gap of the “natural” LP-relaxation of the problem (this fact was obser... |

111 | E.: Frugal path mechanisms
- Archer, Tardos
- 2002
(Show Context)
Citation Context ...ath auctions; Hershberger and Suri [55] and Feigenbaum et al. [35] study methods to make this mechanism efficiently computable and practical in this setting. However, as observed by Archer and Tardos =-=[6]-=-, the VCG mechanism (and, in fact, all min function mechanisms) can force the auctioneer to pay far more than the true cost of the cheapest path. The tendency to overpay is exaggerated in path auction... |

109 | E.: An approximate truthful mechanism for combinatorial auctions with single parameter agents
- Archer, Papadimitriou, et al.
- 2003
(Show Context)
Citation Context ...e bounds converge quite quickly. Mechanisms that are truthful in a randomized sense (that is, in expectation, or with high probability) have been a subject of research in theoretical computer science =-=[4, 5]-=-. These mechanisms seek to encourage truthfulness by introducing randomization into the mechanism. Our results are of a different flavor. We show that one can conclude statements regarding truthfulnes... |

99 |
Markets with a continuum of traders
- Aumann
- 1964
(Show Context)
Citation Context ...ts in the literature study the core of markets and conclude that, under certain conditions, the size of the core shrinks as the size of the market grows (see, for example, the seminal paper of Aumann =-=[10]-=- or the book by Hildenbrand [56]). The set of stable matchings is the core of the stable marriage game, but our market setting is quite different from that in the literature. In fact, in our setting, ... |

96 | Vickrey prices and shortest paths: What is an edge worth
- Hershberge, Suri
(Show Context)
Citation Context ...ds to buy a set of edges, called a flow, capable of routing his demand between the source and the sink. Nisan and Ronen [89] proposed applying the VCG mechanism to path auctions; Hershberger and Suri =-=[55]-=- and Feigenbaum et al. [35] study methods to make this mechanism efficiently computable and practical in this setting. However, as observed by Archer and Tardos [6], the VCG mechanism (and, in fact, a... |

89 | Competitive Generalized Auctions
- Fiat, Goldberg, et al.
(Show Context)
Citation Context ...the optimal revenue is called the competitive ratio of the mechanism, and the goal is to maximize this ratio. This framework has been used to design truthful auctions for the single-unit demand case. =-=[37, 46, 48, 50, 54]-=-. 1 This chapter follows the competitive framework introduced by Goldberg, Hartline, and Wright [50]. We design truthful mechanisms for profit maximization in markets in both the limited demand case a... |

84 |
Urn Models and Their Applications: An Approach to Modern Discrete Probability Theory
- Johnson, Kotz
- 1977
(Show Context)
Citation Context ... occupancy problem, m balls are 152sdistributed amongst n bins. The distribution of the number of balls that end up in each bin has been studied extensively from the perspective of probability theory =-=[67]-=-. We denote the occupancy problem with m balls and n bins by the (m, n)-occupancy problem. The following lemma establishes the connection between the number of singles in the stable marriage game and ... |

82 | Competitive auctions
- Goldberg, Hartline, et al.
- 2006
(Show Context)
Citation Context ...ize the ratio between the revenue 17sof an auction to the revenue of an omniscient auctioneer (that is, an auctioneer who knows the valuations of the bidders). In a sequence of works, Goldberg et al. =-=[49, 48, 50]-=- and Hartline and McGrew [54] use this framework to design highrevenue truthful auctions without any assumption on the bidders’ valuations. All of these results employ randomization in the computation... |

81 |
The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design,” American Economic Review
- Peranson
- 1999
(Show Context)
Citation Context ...t and decentralizing it. However, it is well-known that in a stable matching mechanism, it is not always in a participant’s self-interest to announce their true preference list. Yet Roth and Peranson =-=[99]-=- observe that in practice in the NRMP, very few participants have incentives to lie. They suggest that this phenomenon is due to the fact that the length of the medical students’ preference lists is n... |

80 | Multi-unit Auctions with Budget-constrained Bidders,” EC’05
- Borgs, Chayes, et al.
- 2005
(Show Context)
Citation Context ...demand are based on joint work with Aggarwal, Fiat, Goldberg, Hartline, and Sudan [2]. The results regarding budget-constrained bidders are based on joint work with Borgs, Chayes, Mahdian, and Saberi =-=[14]-=-. 3 It is standard to assume that bidders trust the auctioneer to implement the announced mechanism and so one might argue that trusting the auctioneer’s random source is not unreasonable. However, an... |

77 | 2001): “A crash course in implementation theory
- Jackson
(Show Context)
Citation Context ..., they believe will maximize their own gain. The field of mechanism design or implementation theory attempts to build systems taking into consideration the strategic behavior of the participants (see =-=[62, 63]-=- for a survey). The basic paradigm postulates that each individual maintains some private information relevant to the problem at hand. A system solicits from participants their private information and... |

73 |
Machiavelli and the GaleShapley algorithm
- Dubins, Freedman
- 1981
(Show Context)
Citation Context ...any stable marriage mechanism, each player has an optimal strategy which is simply a truncation (a prefix) of his true preference list. The following theorem (due to Roth [95] and Dubins and Freedman =-=[24]-=-) shows that in deferred acceptance mechanisms, truthfulness is a dominant strategy for half the population. Theorem 5.1.4 In the men-optimal stable marriage mechanism, truth-telling is a dominant str... |

67 |
Irrationality in game theory
- Aumann
- 1992
(Show Context)
Citation Context ...dget balance, we usually require cost allocations and cost-sharing schemes to satisfy additional properties. One property that is extensively studied in the classic cooperative game theory literature =-=[8, 13, 43, 103, 108, 109]-=- is the property of being in the core, first suggested by Edgeworth [28] in 1881. This property intuitively says that no subset of agents should be overcharged for the service. Definition 13 A cost al... |

66 | On certain connectivity properties of the internet topology
- Mihail, Papadimitriou, et al.
- 2003
(Show Context)
Citation Context ...nism has small overpayments. Tawlar [111] and Garg et al. [42] consider restricting the setting by imposing a structure on the collection of feasible sets of agents. Mihail, Papadimitriou, and Saberi =-=[81]-=- show that in a random graph, the expected payment of a VCG mechanism for a shortest path is small. Feigenbaum et al. [35] measure the average overpayment of the VCG mechanism for shortest path auctio... |

63 | Frugality in path auctions
- Elkind, Sahai, et al.
- 2004
(Show Context)
Citation Context ...tions because a bonus needs to be paid to every agent on the path. Thus, the payment to the lowest-cost path may even greatly exceed the cost of the second-cheapest path. Elkind, Sahai, and Steiglitz =-=[29]-=- generalized the result of Archer and Tardos [6] to prove that all truthful mechanisms have high overpayments. As motivated by the work of Elkind, Sahai, and Steiglitz [29], to reduce the payment we m... |

60 | Knapsack Auctions
- Aggarwal, Hartline
- 2006
(Show Context)
Citation Context ...so the existence of a deterministic mechanism remains an open question. The results of this chapter regarding limited demand are based on joint work with Aggarwal, Fiat, Goldberg, Hartline, and Sudan =-=[2]-=-. The results regarding budget-constrained bidders are based on joint work with Borgs, Chayes, Mahdian, and Saberi [14]. 3 It is standard to assume that bidders trust the auctioneer to implement the a... |