Shutting-out-proofness in object allocation problems with money

We study the problem of allocating heterogeneous objects to agents with money. Each agent can receive several objects and has a quasi-linear utility function. The owner of the objects is only interested in his revenue from an allocation. An (allocation) rule is shutting-out-proof if no group of agents together with the owner ever benefits from shutting out other groups of agents and arranging payments among themselves. We show that on any domain that includes all the additive valuation functions, a Vickrey rule satisfies shutting-out-proofness if and only if all the valuation functions in the domain satisfy the substitutes condition (Kelso and Crawford, 1982). Our result sheds a new light on the relationship between the desirable properties of a Vickrey rule and the substitutes condition (Ausubel and Milgrom, 2002; Milgrom, 2004).

Hitotsubashi Institute for Advanced Study, Hitotsubashi University

2024-02-13

English(eng)

technical report

VoR

35

The author gratefully acknowledges financial support from the Japan society for the Promotion of Sciences (23K18777).

Discussion paper series / Hitotsubashi Institute for Advanced Study, Hitotsubashi University

https://hdl.handle.net/10086/82185