Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Constructive Approach to Reduced-Form Auctions with Applications to
  Multi-Item Mechanism Design   We provide a constructive proof of Border's theorem [Bor91, HR15a] and its
generalization to reduced-form auctions with asymmetric bidders [Bor07, MV10,
CKM13]. Given a reduced form, we identify a subset of Border constraints that
are necessary and sufficient to determine its feasibility. Importantly, the
number of these constraints is linear in the total number of bidder types. In
addition, we provide a characterization result showing that every feasible
reduced form can be induced by an ex-post allocation rule that is a
distribution over ironings of the same total ordering of the union of all
bidders' types.
  We show how to leverage our results for single-item reduced forms to design
auctions with heterogeneous items and asymmetric bidders with valuations that
are additive over items. Appealing to our constructive Border's theorem, we
obtain polynomial-time algorithms for computing the revenue-optimal auction.
Appealing to our characterization of feasible reduced forms, we characterize
feasible multi-item allocation rules.

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The categories of this paper are: stat
30
The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
2
The categories of this paper are: math
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph