## An impossibility result for ex-post implementable multi-item auctions with private values (2007)

Citations: | 2 - 1 self |

### BibTeX

@TECHREPORT{Lavi07animpossibility,

author = {Ron Lavi and Noam Nisan},

title = {An impossibility result for ex-post implementable multi-item auctions with private values},

institution = {},

year = {2007}

}

### OpenURL

### Abstract

We analyze ex-post implementable social choice functions for private-value and quasi-linear settings over restricted domains of preferences, the leading example being multi-item auctions (with either heterogeneous or homogeneous goods). Our work generalizes the characterization of Roberts (1979) who characterized ex-post implementability over unrestricted domains. We show that ex-post implementability for multi-item auctions (and related restricted domains) implies weighted welfare maximization, if the given function also satisfies four additional social choice requirements. The most significant requirement is similar to Arrow’s IIA condition, adjusted to the quasi-linear case, and we study its connection to various existing monotonicity properties.

### Citations

1208 | Counterspeculation, Auctions, and Competitive Sealed Tenders - Vickrey - 1961 |

935 |
Optimal Auction Design
- Myerson
- 1981
(Show Context)
Citation Context ...oals, to the impossibility of doing so, turns out to be strongly related to the dimensionality of the domain of preferences being considered. On the one hand, Myerson’s simple monotonicity condition (=-=Myerson, 1981-=-), that completely characterizes ex-post implementability in single-dimensional domains, gives rise to many implementable social choice functions. For example, this monotonicity enables revenue-maximi... |

726 |
Social Choice and Individual Values
- Arrow
- 1951
(Show Context)
Citation Context ...ion that determines an alternative a ∈ A according to players’ type declaration v ∈ V , where V = V1 ×· · ·×Vn is the domain of player types. Weak-IIA is a translation of Arrow’s well-known property (=-=Arrow, 1951-=-), from the non-quasi-linear setting to the quasi-linear world. It states that, if there exist two types v,v ′ such that f(v) = a and f(v ′ ) = b, then there must exist a player i such that vi(a) �= v... |

704 | Multipart pricing of public goods - Clarke - 1971 |

575 | Incentives in team - Groves - 1973 |

351 |
Strategy-Proofness and Arrow’s Conditions: Existence and Correspondence theorems for Voting Procedures and Social Welfare Functions
- Satterthwaite
- 1975
(Show Context)
Citation Context ...main; see the survey of Le Breton and Weymark (2004) for more examples). On the other hand, if preferences are completely unrestricted, the classic Gibbard-Satterthwaite impossibility (Gibbard, 1973; =-=Satterthwaite, 1975-=-) states that dictatorship is the only implementable social choice function. The proof makes extensive use of Arrow’s theorem, and in fact follows a very similar pattern to the first part of our proof... |

247 |
Gibbard, A.: Manipulation of voting schemes: a general result
- Gibbard
- 1973
(Show Context)
Citation Context ...ingle-peaked domain; see the survey of Le Breton and Weymark (2004) for more examples). On the other hand, if preferences are completely unrestricted, the classic Gibbard-Satterthwaite impossibility (=-=Gibbard, 1973-=-; Satterthwaite, 1975) states that dictatorship is the only implementable social choice function. The proof makes extensive use of Arrow’s theorem, and in fact follows a very similar pattern to the fi... |

183 | Truth revelation in approximately efficient combinatorial auctions - Lehmann, O’Callaghan, et al. - 2002 |

138 | Combinatorial auctions with decreasing marginal utilities - Lehmann, Lehmann, et al. - 2006 |

115 | 2006): “The communication requirements of efficient allocations and supporting prices - Nisan, Segal |

108 | Frugal path mechanisms - Archer, Tardos |

107 |
Optimal allocation of public goods: A solution to the ‘free-rider’ problem
- Groves, Ledyard
- 1977
(Show Context)
Citation Context ...nue-maximization in single-item auctions (Myerson, 1981), asymptotically efficient and dominant-strategy double auctions (McAfee, 1992), dominant-strategy and budget-balanced cost sharing mechanisms (=-=Groves and Ledyard, 1977-=-), and competitive auctions for unlimited supply of items (Goldberg, Hartline, Karlin, Saks and Wright, 2006), among many other positive results that we do not list. Therefore, in singledimensional do... |

102 | Nash equilibrium and welfare optimality - Maskin - 1999 |

94 | The characterization of implementable choice rules - Roberts - 1979 |

90 | Incentive compatible multi unit combinatorial auctions - Bartal, Gonen, et al. - 2003 |

85 | Truthful and near-optimal mechanism design via linear programming - Lavi, Swami - 2005 |

79 | Truthful randomized mechanisms for combinatorial auctions - Dobzinski, Nisan, et al. - 2006 |

68 | A Necessary and Sufficient Condition for Rationalizability in a Quasi-Linear Context - Rochet - 1987 |

66 |
A Dominant Strategy Double Auction
- McAfee
- 1992
(Show Context)
Citation Context ...ementable social choice functions. For example, this monotonicity enables revenue-maximization in single-item auctions (Myerson, 1981), asymptotically efficient and dominant-strategy double auctions (=-=McAfee, 1992-=-), dominant-strategy and budget-balanced cost sharing mechanisms (Groves and Ledyard, 1977), and competitive auctions for unlimited supply of items (Goldberg, Hartline, Karlin, Saks and Wright, 2006),... |

54 | Robust mechanism design
- Bergemann, Morris
- 2005
(Show Context)
Citation Context ...6) notes. Second, we very briefly point out that the solution concept of ex-post implementation has received much attention in the recent literature, under the framework of “robust mechanism design” (=-=Bergemann and Morris, 2005-=-). Wilson’s critique (Wilson, 1987) on the alternative notion of Bayesian implementability states that the usual common-prior assumption is a too strong assumption to make, and in that sense detail-fr... |

52 | Multidimensional incentive compatibility and mechanism design - McAfee, McMillan - 1988 |

52 | Weak monotonicity suffices for truthfulness on convex domains - Saks, Yu - 2005 |

51 | Auctions and Privatization - Maskin - 1992 |

48 | Weak monotonicity characterizes deterministic dominant-strategy implementation - Bikhchandani, Chatterji, et al. - 2006 |

45 | Bundling equilibrium in combinatorial auctions - Holzman, Kfir-Dahav, et al. |

36 | Truthful mechanism design for multi-dimensional scheduling via cycle monotonicity - Lavi, Swami - 2007 |

24 | Strategy-Proof Allocation Mechanisms at Differentiable Points,” The Review of Economic Studies - Satterthwaite, Sonnenschein - 1981 |

12 | Ex Post Implementation in Environments with Private Goods - Bikhchandani - 2006 |

7 | Zame (2006): \The Limits of Ex Post Implementation - Jehiel, Moldovanu, et al. |

5 | Characterization of Ex Post Equilibrium - Holzman, Monderer |

5 | Arrovian Social Choice Theory on Economic Domains - Breton, Weymark - 2011 |