Robust trading mechanisms over 0/1 polytopes

Mustafa Ç. Pınar ()
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Mustafa Ç. Pınar: Bilkent University

Journal of Combinatorial Optimization, 2018, vol. 36, issue 3, No 9, 845-860

Abstract: Abstract The problem of designing a trade mechanism (for an indivisible good) between a seller and a buyer is studied in the setting of discrete valuations of both parties using tools of finite-dimensional optimization. A robust trade design is defined as one which allows both traders a dominant strategy implementation independent of other traders’ valuations with participation incentive and no intermediary (i.e., under budget balance). The design problem which is initially formulated as a mixed-integer non-linear non-convex feasibility problem is transformed into a linear integer feasibility problem by duality arguments, and its explicit solution corresponding to posted price optimal mechanisms is derived along with full characterization of the convex hull of integer solutions. A further robustness concept is then introduced for a central planner unsure about the buyer or seller valuation distribution, a corresponding worst-case design problem over a set of possible distributions is formulated as an integer linear programming problem, and a polynomial solution procedure is given. When budget balance requirement is relaxed to feasibility only, i.e., when one allows an intermediary maximizing the expected surplus from trade, a characterization of the optimal robust trade as the solution of a simple linear program is given. A modified VCG mechanism turns out to be optimal.

Keywords: Mechanism design; Bilateral trade; Robustness; Integer programming; Duality; VCG mechanism (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-017-0177-2

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