### Resumé

Sprog | Engelsk |
---|---|

Tidsskrift | Statistica Neerlandica |

Vol/bind | 61 |

Udgave nummer | 1 |

Sider | 156–171 |

ISSN | 0039-0402 |

DOI | |

Status | Udgivet - 2007 |

Udgivet eksternt | Ja |

### Emneord

- Equilibria
- VCG outcome
- Buyers-are-substitutes condition
- Concavity

### Citer dette

*Statistica Neerlandica*,

*61*(1), 156–171. DOI: 10.1111/j.1467-9574.2007.00356.x

}

*Statistica Neerlandica*, bind 61, nr. 1, s. 156–171. DOI: 10.1111/j.1467-9574.2007.00356.x

**Note on the Applicability of the VCG Mechanism to Capacitated Assignment Problems and Extensions.** / Lok, Reinder B.; Morales, Dolores Romero; Vermeulen, Dries.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

TY - JOUR

T1 - Note on the Applicability of the VCG Mechanism to Capacitated Assignment Problems and Extensions

AU - Lok,Reinder B.

AU - Morales,Dolores Romero

AU - Vermeulen,Dries

PY - 2007

Y1 - 2007

N2 - For the allocation of heterogeneous items, it is known that the buyers-are-substitutes condition is necessary and sufficient to ensure that a pricing equilibrium can yield the same allocation and payments as the VCG mechanism. Furthermore, concavity of the corresponding transferable utility TU-game guarantees that this VCG outcome can also be achieved by an ascending price auction. We show that concavity, and hence the buyers-are-substitutes condition, holds for the TU-game of the assignment problem with general capacities. Therefore, the VCG mechanism is supported by a pricing equilibrium which can also be achieved by an ascending auction. We also show that the buyers-are-substitutes condition, and hence concavity, does not hold anymore for very natural and straightforward extensions of this problem. This shows that the necessity of the substitutes property is a considerable restriction on the applicability of the VCG mechanism.

AB - For the allocation of heterogeneous items, it is known that the buyers-are-substitutes condition is necessary and sufficient to ensure that a pricing equilibrium can yield the same allocation and payments as the VCG mechanism. Furthermore, concavity of the corresponding transferable utility TU-game guarantees that this VCG outcome can also be achieved by an ascending price auction. We show that concavity, and hence the buyers-are-substitutes condition, holds for the TU-game of the assignment problem with general capacities. Therefore, the VCG mechanism is supported by a pricing equilibrium which can also be achieved by an ascending auction. We also show that the buyers-are-substitutes condition, and hence concavity, does not hold anymore for very natural and straightforward extensions of this problem. This shows that the necessity of the substitutes property is a considerable restriction on the applicability of the VCG mechanism.

KW - Equilibria

KW - VCG outcome

KW - Buyers-are-substitutes condition

KW - Concavity

U2 - 10.1111/j.1467-9574.2007.00356.x

DO - 10.1111/j.1467-9574.2007.00356.x

M3 - Journal article

VL - 61

SP - 156

EP - 171

JO - Statistica Neerlandica

T2 - Statistica Neerlandica

JF - Statistica Neerlandica

SN - 0039-0402

IS - 1

ER -