Bilateral k+1-price Auctions with Asymmetric Shares and Values

38 Pages Posted: 10 Nov 2011 Last revised: 26 Apr 2014

See all articles by Cédric Wasser

Cédric Wasser

University of Basel - Faculty of Business and Economics

Date Written: June 25, 2013

Abstract

We study a sealed-bid auction between two bidders with asymmetric independent private values. The two bidders own asymmetric shares in a partnership. The higher bidder buys the lower bidder's shares at a per-unit price that is a convex combination of the two bids. The weight of the lower bid is denoted by k in [0,1]. We partially characterize equilibrium strategies and show that they are closely related to equilibrium strategies of two well-studied mechanisms: the double auction between a buyer and a seller and the first-price auction between two buyers (or two sellers). Combining results from those two branches of the literature enables us to prove equilibrium existence. Moreover, we find that there is a continuum of equilibria if k in (0,1) whereas the equilibrium is unique if k in {0,1}. Our approach also suggests a procedure for numerical simulations.

Keywords: Asymmetric auctions, Double auction, First-price auction, Partnership dissolution, Detail-free mechanism

JEL Classification: D44, D82, C78, C72

Suggested Citation

Wasser, Cédric, Bilateral k+1-price Auctions with Asymmetric Shares and Values (June 25, 2013). Available at SSRN: https://ssrn.com/abstract=1957429 or http://dx.doi.org/10.2139/ssrn.1957429

Cédric Wasser (Contact Author)

University of Basel - Faculty of Business and Economics ( email )

Peter Merian-Weg 6
Basel, 4002
Switzerland

HOME PAGE: http://www.cedricwasser.net

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