Private Interdependent Valuations: New Bounds for Single-Item Auctions and Matroids
CoRR(2024)
摘要
We study auction design within the widely acclaimed model of interdependent
values, introduced by Milgrom and Weber [1982]. In this model, every bidder i
has a private signal s_i for the item for sale, and a public valuation
function v_i(s_1,…,s_n) which maps every vector of private signals (of
all bidders) into a real value. A recent line of work established the existence
of approximately-optimal mechanisms within this framework, even in the more
challenging scenario where each bidder's valuation function v_i is also
private. This body of work has primarily focused on single-item auctions with
two natural classes of valuations: those exhibiting submodularity over signals
(SOS) and d-critical valuations.
In this work we advance the state of the art on interdependent values with
private valuation functions, with respect to both SOS and d-critical
valuations. For SOS valuations, we devise a new mechanism that gives an
improved approximation bound of 5 for single-item auctions. This mechanism
employs a novel variant of an "eating mechanism", leveraging LP-duality to
achieve feasibility with reduced welfare loss. For d-critical valuations, we
broaden the scope of existing results beyond single-item auctions, introducing
a mechanism that gives a (d+1)-approximation for any environment with matroid
feasibility constraints on the set of agents that can be simultaneously served.
Notably, this approximation bound is tight, even with respect to single-item
auctions.
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