An implementation of the Vickrey outcome with gross-substitutes

Abstract

We consider a market with only one seller and many buyers. The seller owns several indivisible objects on sale. Each buyer can receive many objects and has a gross-substitutes valuation for every package of objects. The gross-substitutes condition guarantees the non-emptiness of the core of the market (Ausubel and Milgrom, 2002). Moreover, the Vickrey outcome (Vickrey, 1961) of the market leads to a core payoff in which each buyer gets his maximum core payoff. The aim of this paper is to analyze the following mechanism. Simultaneously, each buyer requests a package by announcing how much he would pay for it. After all buyers' requests, the seller decides the final assignment of packages and the prices. If a buyer gets a package of objects, it must be his request or an allocation at least as good as his request. The subgame perfect equilibrium outcomes of the mechanism correspond to the Vickrey outcome of the market.