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A Conic Approach to the Implementation of Reduced-Form Allocation Rules

Xu Lang and Zaifu Yang

Discussion Papers from Department of Economics, University of York

Abstract: We examine the implementation of reduced-form allocation rules in mechanism design problems. To handle the problem, we adopt a conic approach which uses a lift-and-project method to construct a projection cone and find its finite generators. This results in a set of implementable reduced forms for implementation. We then characterize projection cones for several typical mechanism design problems including single-item auctions, bilateral trade, compromise, and multiple-item auctions with group capacity constraints. We find that the implementation condition in general has a linear characterization by a class of sign functions, which is larger and richer than the well-known class of characteristic functions found by Border. These results admit meaningful economic interpretations.

Keywords: Implementation; Reduced-form rules; Auction; Bilateral trade; Mechanism design; Total unimodularity. (search for similar items in EconPapers)
JEL-codes: D44 C65 (search for similar items in EconPapers)
Date: 2019-09
New Economics Papers: this item is included in nep-des and nep-ore
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