## Applications of Approximation Algorithms to Cooperative Games (2001)

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Venue: | STOC'01 |

Citations: | 121 - 7 self |

### BibTeX

@MISC{Jain01applicationsof,

author = {Kamal Jain and Vijay V. Vazirani},

title = {Applications of Approximation Algorithms to Cooperative Games},

year = {2001}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

1029 | Multicast routing in a datagram internetwork
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Citation Context ...each receiver. This results in several copies of the same message traversing the network links. This waste of bandwidth could be avoided by using a different form of routing, called multicast routing =-=[4]-=-. Multicast routing uses a tree connecting all the receivers to the source. The source sends one copy of the message to each neighboring vertex in the tree. These vertices further act as sources for t... |

952 |
Approximation Algorithms
- Vazirani
- 2001
(Show Context)
Citation Context ...[7] and Fekete and Pulleyblank [9], respectively. Several NP-hard minimization problems admit a constant factor approximation algorithm based on an LP-relaxation that is a covering program (e.g., see =-=[32]-=-). In Section 5 we study general approaches for analyzing games based on such problems. We show that the cost function given by an optimal solution to a covering linear program satisfies the covering ... |

677 | Worst-Case Equilibria
- Koutsoupias, Papadimitriou
- 1999
(Show Context)
Citation Context ...nd approximation algorithms share common methodology -- both heavily use machinery from the theory of linear programming. Various aspects of this connection have been explored recently by researchers =-=[8, 10, 15, 20, 21, 26, 27, 29]. In this -=-paper we will consider the problem of sharing the cost of a jointly utilized facility in a "fair" manner. Consider a service providing company whose set of possible customers, also called us... |

577 | Algorithmic mechanism design
- Nisan, Ronen
- 1999
(Show Context)
Citation Context ...nd approximation algorithms share common methodology -- both heavily use machinery from the theory of linear programming. Various aspects of this connection have been explored recently by researchers =-=[8, 10, 15, 20, 21, 26, 27, 29]. In this -=-paper we will consider the problem of sharing the cost of a jointly utilized facility in a "fair" manner. Consider a service providing company whose set of possible customers, also called us... |

540 |
A value for n-person games
- Shapley
- 1953
(Show Context)
Citation Context ...sharing methods. It is useful to characterize methods from this class possessing special properties so that the service provider may pick one judiciously. Two well known methods are: 1. Shapley Value =-=[31]-=-: In the context of multicasting (see Section 2), this method distributes the cost of each edge equally among all the users located downstream of the edge. Moulin and Shenker show that this method ach... |

264 | Sharing the cost of multicast transmissions
- Feigenbaum, Papadimitriou, et al.
(Show Context)
Citation Context ...nd approximation algorithms share common methodology -- both heavily use machinery from the theory of linear programming. Various aspects of this connection have been explored recently by researchers =-=[8, 10, 15, 20, 21, 26, 27, 29]. In this -=-paper we will consider the problem of sharing the cost of a jointly utilized facility in a "fair" manner. Consider a service providing company whose set of possible customers, also called us... |

259 |
A fast algorithm for Steiner trees
- Kou, Markowsky, et al.
- 1981
(Show Context)
Citation Context ...ee. We get around these difficulties by turning to approximation algorithms. A well known factor 2 approximation algorithm for Steiner tree is to find a minimum spanning tree on the required vertices =-=[19]-=-. The minimum spanning tree game has been studied extensively in the literature [2, 11, 12, 17, 18, 16]. Kent and Skorin-Kapov [17] show how to construct a whole class of weak cross-monotonic methods ... |

167 | Strategyproof Sharing of Submodular Costs: Budget Balance versus Efficiency.” Economic Theory 18
- Moulin, Shenker
- 2001
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Citation Context ... options: sacrifice either budget balance or efficiency. In the first case, one can show that if the cost function is nondecreasing and submodular, then there is only one way of maximizing efficiency =-=[24]-=-. This is called the marginal cost mechanism. This mechanism is strategyproof, though not group strategyproof. It never creates a budget surplus but can run a deficit, and in many cases raises no reve... |

139 |
On Balanced Sets and Cores
- Shapley
- 1967
(Show Context)
Citation Context ...perty if for any set S of users and any covering of S of the form S = S j f j \Delta S j , we have C(S)sP j f j \Delta C(S j ), where each S j is a set of users. The classic Bondareva-Shapley Theorem =-=[3, 30]-=- shows that a necessary and sufficient condition for the existence of a weakly cross-monotonic cost sharing method is that the underlying cost function exhibit the covering property. Does a cost funct... |

103 |
The characterization of implementable choice rules
- Roberts
- 1979
(Show Context)
Citation Context ...r all subsets, S, the sum of the utilities of users in S minus C(S). Ideally, one seeks an efficient, budget balanced and group strategyproof cost sharing mechanism. A classical result in game theory =-=[13, 28]-=- shows that such a mechanism does not exist even for a submodular cost function (see Section 2 for formal definitions of these notions). Such a mechanism does not exist even after relaxing the conditi... |

64 |
A concept of egalitarianism under participation constraints
- Dutta, Ray
- 1989
(Show Context)
Citation Context ...e equally among all the users located downstream of the edge. Moulin and Shenker show that this method achieves the lowest worst case loss of efficiency over all utility profiles [24]. 2. Egalitarian =-=[5]-=-: This method, due to Dutta and Ray, seeks to distribute the cost equally among all the receivers. Mutuswami has shown that assuming all users draw their utility values from the same probability distr... |

60 |
Incremental cost sharing: Characterization by coalition strategy-proofness
- Moulin
- 1999
(Show Context)
Citation Context ...ough not group strategyproof. It never creates a budget surplus but can run a deficit, and in many cases raises no revenue at all [24]. In the second case, a fundamental theorem of Moulin and Shenker =-=[23, 24]-=- shows that a cross-monotonic cost sharing method (also known as population monotonic allocation scheme, see Section 2 for a definition) gives rise to a budget balance and group strategyproofness cost... |

49 | Cooperative facility location games
- Goemans, Skutella
(Show Context)
Citation Context |

46 |
On cost allocation for a spanning tree: A game theoretic approach, Networks 6
- Bird
- 1976
(Show Context)
Citation Context ...known factor 2 approximation algorithm for Steiner tree is to find a minimum spanning tree on the required vertices [19]. The minimum spanning tree game has been studied extensively in the literature =-=[2, 11, 12, 17, 18, 16]-=-. Kent and Skorin-Kapov [17] show how to construct a whole class of weak cross-monotonic methods as well as one cross-monotone method for this game. For the latter result, they use matroid properties ... |

45 |
Minimum cost spanning tree games
- Granot, Huberman
- 1981
(Show Context)
Citation Context ...known factor 2 approximation algorithm for Steiner tree is to find a minimum spanning tree on the required vertices [19]. The minimum spanning tree game has been studied extensively in the literature =-=[2, 11, 12, 17, 18, 16]-=-. Kent and Skorin-Kapov [17] show how to construct a whole class of weak cross-monotonic methods as well as one cross-monotone method for this game. For the latter result, they use matroid properties ... |

38 | S.: Optimization problems in congestion control
- Karp, Koutsoupias, et al.
- 2000
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Citation Context |

36 | Algorithms for Selfish Agents: Mechanism Design for Distributed Computation
- Nisan
- 1999
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Citation Context |

34 | Fairness measures for resource allocation
- Kumar
- 2000
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Citation Context |

28 |
On the core and nucleolus of the minimum cost spanning tree games
- Granot, Huberman
- 1984
(Show Context)
Citation Context ...known factor 2 approximation algorithm for Steiner tree is to find a minimum spanning tree on the required vertices [19]. The minimum spanning tree game has been studied extensively in the literature =-=[2, 11, 12, 17, 18, 16]-=-. Kent and Skorin-Kapov [17] show how to construct a whole class of weak cross-monotonic methods as well as one cross-monotone method for this game. For the latter result, they use matroid properties ... |

28 |
Population monoton cost allocation on mst's
- Kent, Skorin-Kapov
- 1996
(Show Context)
Citation Context |

25 |
On finding integer solutions to linear programs
- Balinski
- 1966
(Show Context)
Citation Context ... the facility location game seems particularly interesting. Recently, Goemans and Skutella [10] have studied this game and have a core allocation in case the well known LP-relaxation, due to Balinski =-=[1]-=-, has an integral solution. Finally, we consider the purely combinatorial question of characterizing the space of cross-monotone methods corresponding to a given nondecreasing submodular function. We ... |

13 |
Some applications of linear programming to cooperative games
- Bondareva
- 1963
(Show Context)
Citation Context ...perty if for any set S of users and any covering of S of the form S = S j f j \Delta S j , we have C(S)sP j f j \Delta C(S j ), where each S j is a set of users. The classic Bondareva-Shapley Theorem =-=[3, 30]-=- shows that a necessary and sufficient condition for the existence of a weakly cross-monotonic cost sharing method is that the underlying cost function exhibit the covering property. Does a cost funct... |

10 |
Cost allocation for steiner trees
- Megiddo
- 1978
(Show Context)
Citation Context ...ers may be arbitrarily more costly than the cheapest tree to them. The latter of course is an optimal Steiner tree containing S and the source. Such a tree is NP-hard to compute. In addition, Megiddo =-=[22]-=- has shown that for this game, the core is empty and so there does not even exist a weak cross-monotonic cost sharing method for the optimal Steiner tree. We get around these difficulties by turning t... |

10 |
bad is selfish routing
- How
(Show Context)
Citation Context |

9 | On approximately fair cost allocation for Euclidean TSP games
- Faigle, Fekete, et al.
- 1998
(Show Context)
Citation Context ...en problem of deriving a factor 1.5 solution, using Christofedes' algorithm. Core allocation functions for the metric and Euclidean TSP games have been given by Faigle, Fekete, Hochstattler, and Kern =-=[7]-=- and Fekete and Pulleyblank [9], respectively. Several NP-hard minimization problems admit a constant factor approximation algorithm based on an LP-relaxation that is a covering program (e.g., see [32... |

7 |
Algorithms for sel agents - mechanism design for distributed computation
- Nisan
- 1999
(Show Context)
Citation Context ...and approximation algorithms share common methodology { both heavily use machinery from the theory of linear programming. Various aspects of this connection have been explored recently by researchers =-=[8, 10, 15, 20, 21, 26, 27, 29]-=-. In this paper we will consider the problem of sharing the cost of a jointly utilized facility in a \fair" manner. Consider a service providing company whose set of possible customers, also called us... |

3 |
Partial equilibirium approach to the free rider problem
- Green, Kohlberg, et al.
- 1976
(Show Context)
Citation Context ...r all subsets, S, the sum of the utilities of users in S minus C(S). Ideally, one seeks an efficient, budget balanced and group strategyproof cost sharing mechanism. A classical result in game theory =-=[13, 28]-=- shows that such a mechanism does not exist even for a submodular cost function (see Section 2 for formal definitions of these notions). Such a mechanism does not exist even after relaxing the conditi... |

3 |
Strategyproof mechanism for cost sharing. working paper, Indian statistical Institute
- Mutuswami
(Show Context)
Citation Context ...tuswami has shown that assuming all users draw their utility values from the same probability distribution (with some technical restrictions) this method maximizes the expected size of the set served =-=[25]-=-. A cost sharing method is said to satisfy the coalition participation constraint if the total cost share of any subset S of the users is no more than C(S), i.e., coalition S has no incentive to break... |

2 |
Distance monotonic stable cost allocation scheme for the minimum cost spanning tree network
- Kent, Skorin-Kapov
- 1997
(Show Context)
Citation Context |

2 | bad is sel sh routing - How - 2000 |

1 |
A note on the traveling preacher problem. submitted to, Operations Research Letter
- Fekete, Pulleyblank
(Show Context)
Citation Context ... 1.5 solution, using Christofedes' algorithm. Core allocation functions for the metric and Euclidean TSP games have been given by Faigle, Fekete, Hochstattler, and Kern [7] and Fekete and Pulleyblank =-=[9]-=-, respectively. Several NP-hard minimization problems admit a constant factor approximation algorithm based on an LP-relaxation that is a covering program (e.g., see [32]). In Section 5 we study gener... |

1 |
Group strategyproof cost allocation under a broader notion of a egalitarianism
- Jain, Vazirani
(Show Context)
Citation Context ...er, i. The service provider now has a choice of methods. For instance, he could use his estimates of the probability distribution functions of users' utilities as the mappings. In a forthcoming paper =-=[14]-=- we build on the above idea of running a primal-dual-type algorithm and distributing costs according to n mappings for constructing a class of cross-monotonic cost sharing methods for an arbitrary non... |

1 |
On the core of the minimum steiner tree game in networks
- Kent, Skorin-Kapov
- 1995
(Show Context)
Citation Context |

1 | La ont. Partial equilibirium approach to the free rider problem - Green, Kohlberg, et al. - 1976 |

1 | Algorithms for sel sh agents - mechanism design for distributed computation - Nisan - 1999 |

1 |
bad is sel routing
- How
- 2000
(Show Context)
Citation Context ...and approximation algorithms share common methodology { both heavily use machinery from the theory of linear programming. Various aspects of this connection have been explored recently by researchers =-=[8, 10, 15, 20, 21, 26, 27, 29]-=-. In this paper we will consider the problem of sharing the cost of a jointly utilized facility in a \fair" manner. Consider a service providing company whose set of possible customers, also called us... |