## Frugal path mechanisms (2002)

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Citations: | 108 - 2 self |

### BibTeX

@INPROCEEDINGS{Archer02frugalpath,

author = {Aaron Archer and Éva Tardos},

title = {Frugal path mechanisms},

booktitle = {},

year = {2002},

pages = {991--999}

}

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### Abstract

We consider the problem of selecting a low cost s − t path in a graph, where the edge costs are a secret known only to the various economic agents who own them. To solve this problem, Nisan and Ronen applied the celebrated Vickrey-Clarke-Groves (VCG) mechanism, which pays a premium to induce the edges to reveal their costs truthfully. We observe that this premium can be unacceptably high. There are simple instances where the mechanism pays Θ(k) times the actual cost of the path, even if there is an alternate path available that costs only (1 + ɛ) times as much. This inspires the frugal path problem, which is to design a mechanism that selects a path and induces truthful cost revelation without paying such a high premium. This paper contributes negative results on the frugal path problem. On two large classes of graphs, including ones having three node-disjoint s − t paths, we prove that no reasonable mechanism can always avoid paying a high premium to induce truthtelling. In particular, we introduce a general class of min function mechanisms, and show that all min function mechanisms can be forced to overpay just as badly as VCG. On the other hand, we prove that (on two large classes of graphs) every truthful mechanism satisfying some reasonable properties is a min function mechanism. 1

### Citations

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Citation Context ...send something through the network between nodes s and t, and the teams are s − t paths. The catch is, an agent’s cost is a secret known only to that agent. One can apply the celebrated VCG mechanism =-=[25, 4, 11]-=- to select the team that can perform the task while incurring the minimum cost to itself. However, the total amount that the mechanism must pay to the members of this team can be very high. In the net... |

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Citation Context ...send something through the network between nodes s and t, and the teams are s − t paths. The catch is, an agent’s cost is a secret known only to that agent. One can apply the celebrated VCG mechanism =-=[25, 4, 11]-=- to select the team that can perform the task while incurring the minimum cost to itself. However, the total amount that the mechanism must pay to the members of this team can be very high. In the net... |

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Citation Context ...send something through the network between nodes s and t, and the teams are s − t paths. The catch is, an agent’s cost is a secret known only to that agent. One can apply the celebrated VCG mechanism =-=[25, 4, 11]-=- to select the team that can perform the task while incurring the minimum cost to itself. However, the total amount that the mechanism must pay to the members of this team can be very high. In the net... |

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Citation Context ...al amount that the mechanism must pay to the members of this team can be very high. In the network example, the cheapest team is just the shortest path with respect to the edge costs. Nisan and Ronen =-=[19]-=- indeed applied the VCG mechanism to solve this shortest path problem. One drawback to the VCG mechanism when applied to the shortest path problem is that it can be forced to pay a huge amount, compar... |

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Citation Context ...sociated computational issues. The papers [1, 4, 12, 19] address computational di#culties with the VCG mechanism. The topic of revenue maximizing auctions has received a huge amount of attention. See =-=[14]-=- for a recent text on auction theory, or [6] for a survey on combinatorial auctions. Feigenbaum et al. [8] performed some experiments to determine how much the VCG mechanism overpays on some artificia... |

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Citation Context ...rization result holds for all graphs with three node-disjoint s − t paths. 2 Related Work Recently there has been a spate of research at the border of economics, game theory and computer science. See =-=[22]-=- for a recent overview. The economics and game theory literature contains an enormous body of work on mechanism design, also called implementation theory or the theory of incentives. See [7, chapter 7... |

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Citation Context ...ional issues. The papers [3, 13, 20] address computational difficulties with the VCG mechanism. The topic of revenue maximizing auctions has received a huge amount of attention. See the recent papers =-=[1, 8, 9, 10, 16, 18, 23, 24]-=-, or [5] for a recent survey on combinatorial auctions. Recent work [6] investigates how much the VCG mechanism overpays on some artificial examples generated from the problem of routing between auton... |

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Citation Context ...anism. The topic of revenue maximizing auctions has received a huge amount of attention. See [14] for a recent text on auction theory, or [6] for a survey on combinatorial auctions. Feigenbaum et al. =-=[8]-=- performed some experiments to determine how much the VCG mechanism overpays on some artificial examples generated from the problem of routing between autonomous systems on the Internet. We will discu... |

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Citation Context ...m design framework to some standard optimization problems in computer science, such as shortest paths and scheduling on unrelated machines, and raised some associated computational issues. The papers =-=[3, 13, 20]-=- address computational difficulties with the VCG mechanism. The topic of revenue maximizing auctions has received a huge amount of attention. See the recent papers [1, 8, 9, 10, 16, 18, 23, 24], or [5... |

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Citation Context ...zing auctions has received a huge amount of attention. See the recent papers [1, 3, 6, 7, 8, 14, 16, 21, 22], or [5] for a recent survey on combinatorial auctions. The issue of frugality is raised in =-=[2]-=-, which presents a truthful mechanism for minimizing makespan on machines with speeds. Their mechanism gives a 3-approximation and pays the machines only a logarithmic factor more than the actual cost... |

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Citation Context ...ional issues. The papers [3, 13, 20] address computational difficulties with the VCG mechanism. The topic of revenue maximizing auctions has received a huge amount of attention. See the recent papers =-=[1, 8, 9, 10, 16, 18, 23, 24]-=-, or [5] for a recent survey on combinatorial auctions. Recent work [6] investigates how much the VCG mechanism overpays on some artificial examples generated from the problem of routing between auton... |

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Citation Context ...0] address computational difficulties with the VCG mechanism. The topic of revenue maximizing auctions has received a huge amount of attention. See the recent papers [1, 8, 9, 10, 16, 18, 23, 24], or =-=[5]-=- for a recent survey on combinatorial auctions. Recent work [6] investigates how much the VCG mechanism overpays on some artificial examples generated from the problem of routing between autonomous sy... |

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Citation Context ...ional issues. The papers [3, 13, 20] address computational difficulties with the VCG mechanism. The topic of revenue maximizing auctions has received a huge amount of attention. See the recent papers =-=[1, 8, 9, 10, 16, 18, 23, 24]-=-, or [5] for a recent survey on combinatorial auctions. Recent work [6] investigates how much the VCG mechanism overpays on some artificial examples generated from the problem of routing between auton... |

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Citation Context ...problem yields this worst-case guarantee if and only if the collection of feasible sets F is what he calls a "frugoid," which is a generalization of a matroid. For combinatorial auctions, La=-=vi et al. [16]-=- prove a characterization result similar in spirit to our Theorems 6.5 and 6.4. Under conditions similar to ours, they prove that a slight generalization of VCG is the only class of truthful mechanism... |

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Citation Context ...m design framework to some standard optimization problems in computer science, such as shortest paths and scheduling on unrelated machines, and raised some associated computational issues. The papers =-=[1, 4, 12, 19]-=- address computational di#culties with the VCG mechanism. The topic of revenue maximizing auctions has received a huge amount of attention. See [14] for a recent text on auction theory, or [6] for a s... |

94 |
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Citation Context ... to ours, they prove that a slight generalization of VCG is the only class of truthful mechanisms for combinatorial auctions. Their characterization theorem is reminiscent of Roberts's classic result =-=[23]-=- that in a general mechanism design problem where the agents' valuations of the outcomes can be arbitrary, a truthful mechanism must select the outcome that maximizes an a#ne function of the valuation... |

93 | Vickrey prices and shortest paths: What is an edge worth
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Citation Context ...m design framework to some standard optimization problems in computer science, such as shortest paths and scheduling on unrelated machines, and raised some associated computational issues. The papers =-=[1, 4, 12, 19]-=- address computational di#culties with the VCG mechanism. The topic of revenue maximizing auctions has received a huge amount of attention. See [14] for a recent text on auction theory, or [6] for a s... |

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Citation Context ...hanisms can be forced to pay #(n) times the actual costs incurred, even in a tight market. Since the original appearance of this paper [3], several authors have followed up on our work. Elkind et al. =-=[7]-=- proved that every truthful mechanism (without any additional assumptions) can be forced to overpay just as badly as VCG in the worst case. That is, they were able to extend our non-frugality result (... |

49 | Linear programming and vickrey auctions
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Citation Context ...m design framework to some standard optimization problems in computer science, such as shortest paths and scheduling on unrelated machines, and raised some associated computational issues. The papers =-=[1, 4, 12, 19]-=- address computational di#culties with the VCG mechanism. The topic of revenue maximizing auctions has received a huge amount of attention. See [14] for a recent text on auction theory, or [6] for a s... |

39 |
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Citation Context ...function mechanisms. Whereas our work examines one interesting mechanism design setting where VCG overpays badly and shows this drawback is inherent to all truthful mechanisms for the problem, Talwar =-=[24]-=- takes an alternate approach of trying to characterize for what problems the VCG mechanism is guaranteed not to overpay by much. In particular, Talwar examines the general team selection 6 problem and... |

37 |
and Éva Tardos. Truthful mechanisms for one-parameter agents
- Archer
- 2001
(Show Context)
Citation Context ...nvestigates how much the VCG mechanism overpays on some artificial examples generated from the problem of routing between autonomous systems on the internet. The issue of frugality was also raised in =-=[2]-=-, which presents a truthful mechanism for minimizing makespan on machines with speeds. Their mechanism gives a 3-approximation and pays the machines only a logarithmic factor more than the actual cost... |

30 | Competitive auctions for multiple digital goods
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- 2001
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Citation Context ...he topic of revenue maximizing auctions has received a huge amount of attention. See the recent papers [1, 8, 9, 10, 16, 18, 23, 24], or [5] for a recent survey on combinatorial auctions. Recent work =-=[6]-=- investigates how much the VCG mechanism overpays on some artificial examples generated from the problem of routing between autonomous systems on the internet. The issue of frugality was also raised i... |

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Citation Context ...m design framework to some standard optimization problems in computer science, such as shortest paths and scheduling on unrelated machines, and raised some associated computational issues. The papers =-=[3, 13, 20]-=- address computational difficulties with the VCG mechanism. The topic of revenue maximizing auctions has received a huge amount of attention. See the recent papers [1, 8, 9, 10, 16, 18, 23, 24], or [5... |

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Citation Context ...y of work on mechanism design, also called implementation theory or the theory of incentives. See [9, chapter 7], [17, chapter 23] or [21, chapter 10] for an introduction to the field, or the surveys =-=[15, 11]-=-. The celebrated Vickrey-Clarke-Groves (VCG) mechanism [25, 5, 10] is the main general positive result here. Nisan and Ronen [20] applied the mechanism design framework to some standard optimization p... |

4 |
On theories of incentive compatible choice with compensation
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Citation Context ...y of work on mechanism design, also called implementation theory or the theory of incentives. See [7, chapter 7], [17, chapter 23] or [21, chapter 10] for an introduction to the field, or the surveys =-=[15, 12]-=-. The celebrated Vickery-Clarke-Groves (VCG) mechanism [25, 4, 11] is the main general positive result here. Nisan and Ronen [19] applied the mechanism design framework to some standard optimization p... |

4 |
Linear programming and vickrey auctions. Unpublished manuscript
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(Show Context)
Citation Context ...ional issues. The papers [11] and [18] address computational di#culties with the VCG mechanism. The topic of revenue maximizing auctions has received a huge amount of attention. See the recent papers =-=[1, 3, 6, 7, 8, 14, 16, 21, 22]-=-, or [5] for a recent survey on combinatorial auctions. The issue of frugality is raised in [2], which presents a truthful mechanism for minimizing makespan on machines with speeds. Their mechanism gi... |

4 |
Combinatorial Auctions: A survey. Unpublished manuscript
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Citation Context ...8] address computational di#culties with the VCG mechanism. The topic of revenue maximizing auctions has received a huge amount of attention. See the recent papers [1, 3, 6, 7, 8, 14, 16, 21, 22], or =-=[5]-=- for a recent survey on combinatorial auctions. The issue of frugality is raised in [2], which presents a truthful mechanism for minimizing makespan on machines with speeds. Their mechanism gives a 3-... |

3 |
Competitive auctions for multicast content. Unpublished manuscript
- Goldberg, Hartline
- 2000
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1 |
and Eric Maskin. The theory of incentives: An overview
- Laffont
(Show Context)
Citation Context ...y of work on mechanism design, also called implementation theory or the theory of incentives. See [7, chapter 7], [17, chapter 23] or [21, chapter 10] for an introduction to the field, or the surveys =-=[15, 12]-=-. The celebrated Vickery-Clarke-Groves (VCG) mechanism [25, 4, 11] is the main general positive result here. Nisan and Ronen [19] applied the mechanism design framework to some standard optimization p... |

1 |
and Eric Maskin. The theory of incentives: An overview
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(Show Context)
Citation Context ... an enormous body of work on mechanism design, also called implementation theory or the theory of incentives. See [15, chapter 23] or [19, chapter 10] for an introduction to the field, or the surveys =-=[13, 10]-=-. The celebrated Vickery-Clarke-Groves (VCG) mechanism [23, 4, 9] is the main general positive result here. Nisan and Ronen [17] applied the mechanism design framework to some standard optimization pr... |