## Beyond VCG: Frugality of truthful mechanisms (2005)

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Venue: | In Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science |

Citations: | 44 - 3 self |

### BibTeX

@INPROCEEDINGS{Karlin05beyondvcg:,

author = {Anna R. Karlin},

title = {Beyond VCG: Frugality of truthful mechanisms},

booktitle = {In Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science},

year = {2005},

pages = {615--626}

}

### Years of Citing Articles

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### Abstract

We study truthful mechanisms for auctions in which the auctioneer is trying to hire a team of agents to perform a complex task, and paying them for their work. As common in the field of mechanism design, we assume that the agents are selfish and will act in such a way as to maximize their profit, which in particular may include misrepresenting their true incurred cost. Our first contribution is a new and natural definition of the frugality ratio of a mechanism, measuring the amount by which a mechanism “overpays”, and extending previous definitions to all monopoly-free set systems. After reexamining several known results in light of this new definition, we proceed to study in detail shortest path auctions and “r-out-of-k sets ” auctions. We show that when individual set systems (e.g., graphs) are considered instead of worst cases over all instances, these problems exhibit a rich structure, and the performance of mechanisms may be vastly different. In particular, we show that the wellknown VCG mechanism may be far from optimal in these settings, and we propose and analyze a mechanism that is always within a constant factor of optimal. 1

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Citation Context ...ver action benefits them most. In particular, they may report a value different from their true cost ci to the auctioneer, in order to increase the payments they receive. The area of mechanism design =-=[17, 22, 25]-=- studies the design of auctions so that no agent, motivated only by self-interest, has an incentive to cheat. A desirable property for mechanisms is that it be in each agent’s best interest to report ... |

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Citation Context ...n which the lowest bidder is awarded the contract and is paid the second-lowest bid; 1 its generalization to the problem of hiring a team of agents and many other problems is called the VCG mechanism =-=[28, 6, 12]-=-. In the VCG mechanism, the feasible set S selected is always the one with lowest total cost b(S) according to the agents’ bids; each agent is then paid the highest amount it could have bid to still b... |

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Citation Context ...n which the lowest bidder is awarded the contract and is paid the second-lowest bid; 1 its generalization to the problem of hiring a team of agents and many other problems is called the VCG mechanism =-=[28, 6, 12]-=-. In the VCG mechanism, the feasible set S selected is always the one with lowest total cost b(S) according to the agents’ bids; each agent is then paid the highest amount it could have bid to still b... |

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Citation Context ...osts and bids, the problem is therefore defined entirely by the set system of feasible sets. Two special cases of this general setting have been studied extensively in the past: (i) In a path auction =-=[22, 4, 8]-=-, the agents own edges of a known graph, and the auctioneer wants to purchase a path between two given nodes s, t. (ii) In a minimum spanning tree (MST) auction [27, 5, 10], the agents again own edges... |

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Citation Context ...ity ratio in all monopoly-free settings, this settles the worst-case frugality ratio of shortest-path auctions on worst-case graphs. However, this worst case in no way applies to all graphs (see e.g. =-=[18, 9]-=-). The frugality ratio of a mechanism should therefore be bounded in terms of properties of the specific set system under consideration (in this case, the specific graph), rather than by the worst cas... |

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Citation Context ... sell a set of items, interacting with multiple parties. Several recent papers have studied the resulting auctions and their properties. We adopt here the general framework of hiring a team of agents =-=[4, 27, 10]-=-: The auctioneer is intent on hiring a team of agents to perform a complex task. Each agent i can perform a simple task at some cost ci known only to himself. Based on the agents’ bids bi, the auction... |

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63 | A.: On Certain Connectivity Properties of the Internet Topology
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Citation Context ...ity ratio in all monopoly-free settings, this settles the worst-case frugality ratio of shortest-path auctions on worst-case graphs. However, this worst case in no way applies to all graphs (see e.g. =-=[18, 9]-=-). The frugality ratio of a mechanism should therefore be bounded in terms of properties of the specific set system under consideration (in this case, the specific graph), rather than by the worst cas... |

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Citation Context ...osts and bids, the problem is therefore defined entirely by the set system of feasible sets. Two special cases of this general setting have been studied extensively in the past: (i) In a path auction =-=[22, 4, 8]-=-, the agents own edges of a known graph, and the auctioneer wants to purchase a path between two given nodes s, t. (ii) In a minimum spanning tree (MST) auction [27, 5, 10], the agents again own edges... |

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Citation Context ...ndeed, path auctions and similar problems have been studied recently from the Bayesian perspective in [8, 7]. By way of contrast, we follow the approach pioneered by Archer, Tardos, Talwar and others =-=[4, 27, 5]-=-, and study the problem of hiring a team from a worst-case perspective. As we have repeatedly seen in computer science, significant insight can be gained from an understanding of worst-case performanc... |

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Citation Context ...d only if the feasible sets F are the bases of a monopoly-free matroid. The proof is quite similar to the one in [27] for frugoids. It depends on the following well-known characterization of matroids =-=[24]-=-: Proposition 6 A collection F of sets forms the bases of a matroid if and only if for every two sets S, T ∈F,thereisa bijection f between S\T and T \S such that S\{e}∪{f(e)} is in F for every e ∈ S \... |

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Citation Context ... sell a set of items, interacting with multiple parties. Several recent papers have studied the resulting auctions and their properties. We adopt here the general framework of hiring a team of agents =-=[4, 27, 10]-=-: The auctioneer is intent on hiring a team of agents to perform a complex task. Each agent i can perform a simple task at some cost ci known only to himself. Based on the agents’ bids bi, the auction... |

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Citation Context ... [25, 26]), and the “price of stability” (see [2]). The problem of hiring a team of agents in complex settings, at minimum total cost, has been shown to have many practical economic applications (see =-=[9, 1, 23, 16, 21]-=- for examples). In particular, the path auction problem we study 3 here has been the subject of a significant amount of prior research. The traditional economics approach to payment minimization (or p... |

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Citation Context ...deal with selfish users, in particular in network settings, there has been a large body of recent work at the intersection of game theory, economic theory and theoretical computer science (see, e.g., =-=[20, 25]-=-). For instance, the seminal paper of Nisan and Ronen [22], which introduced mechanism design to the theoretical computer science community, studied the tradeoffs between agents’ incentives and comput... |

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Citation Context ...unds. As we are interested in a lower bound, we wish to define the cheapest Nash value ν(c) to be the minimum payments by N over all of its Nash Equilibria. Unluckily, as observed by Immorlica et al. =-=[13]-=-, Nash Equilibria often do not exist for first-price auctions. We will discuss this issue in more detail below; however, we can still define the quantity ν(c) analytically based on the intuition we ga... |

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Citation Context |

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Citation Context ...imal Bayesian auction given the prior distributions from which agents’ private values are drawn. Indeed, path auctions and similar problems have been studied recently from the Bayesian perspective in =-=[8, 7]-=-. By way of contrast, we follow the approach pioneered by Archer, Tardos, Talwar and others [4, 27, 5], and study the problem of hiring a team from a worst-case perspective. As we have repeatedly seen... |

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Citation Context ... sell a set of items, interacting with multiple parties. Several recent papers have studied the resulting auctions and their properties. We adopt here the general framework of hiring a team of agents =-=[4, 27, 10]-=-: The auctioneer is intent on hiring a team of agents to perform a complex task. Each agent i can perform a simple task at some cost ci known only to himself. Based on the agents’ bids bi, the auction... |