Multi-Unit Bilateral Trade

Matthias Gerstgrasser, Paul W. Goldberg, Bart de Keijzer, Philip Lazos, Alexander Skopalik

Research output: Working paper

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Abstract

We characterise the set of dominant strategy incentive compatible (DSIC), strongly budget balanced (SBB), and ex-post individually rational (IR) mechanisms for the multi-unit bilateral trade setting. In such a setting there is a single buyer and a single seller who holds a finite number k of identical items. The mechanism has to decide how many units of the item are transferred from the seller to the buyer and how much money is transferred from the buyer to the seller. We consider two classes of valuation functions for the buyer and seller: Valuations that are increasing in the number of units in possession, and the more specific class of valuations that are increasing and submodular.
Furthermore, we present some approximation results about the performance of certain such mechanisms, in terms of social welfare: For increasing submodular valuation functions, we show the existence of a deterministic 2-approximation mechanism and a randomised e/(1-e) approximation mechanism, matching the best known bounds for the single-item setting.
Original languageEnglish
PublisherarXiv.org
Number of pages20
Publication statusPublished - 2019

Cite this

Gerstgrasser, M., Goldberg, P. W., de Keijzer, B., Lazos, P., & Skopalik, A. (2019). Multi-Unit Bilateral Trade. arXiv.org.