A Theory of Auctions with Endogenous Valuations

53 Pages Posted: 27 Mar 2020 Last revised: 10 Aug 2020

See all articles by Alex Gershkov

Alex Gershkov

Hebrew University of Jerusalem

Benny Moldovanu

University of Bonn - Chair of Economic Theory II; Centre for Economic Policy Research (CEPR)

Philipp Strack

Yale, Department of Economics

Mengxi Zhang

Multiple version iconThere are 2 versions of this paper

Date Written: January 19, 2020

Abstract

We derive the revenue maximizing allocation of m units among n symmetric agents who have unit demand, and who take costly actions that influence their values before participating in the mechanism. The allocation problem with costly actions can be represented by a reduced form model where agents have convex, non-expected utility preferences over the interim probability of receiving an object. Both the uniform m+1 price auction and the discriminatory pay-your-bid auction with reserve price constitute symmetric revenue maximizing mechanisms. Contrasting the case with exogenous valuations, the optimal reserve price reacts to both demand and supply. We also identify a condition under which the optimal mechanism is indeed symmetric, and illustrate the structure of the optimal asymmetric mechanism when the condition fails. The main tool in our analysis is an integral inequality, due to Fan and Lorentz (1954), involving majorization, super-modularity and convexity.

Keywords: Auctions, Mechanism Design, Investments, Endogenous Valuations

Suggested Citation

Gershkov, Alex and Moldovanu, Benny and Strack, Philipp and Zhang, Mengxi, A Theory of Auctions with Endogenous Valuations (January 19, 2020). Available at SSRN: https://ssrn.com/abstract=3547465 or http://dx.doi.org/10.2139/ssrn.3547465

Alex Gershkov

Hebrew University of Jerusalem ( email )

Mount Scopus
Jerusalem, Jerusalem 91905
Israel

HOME PAGE: http://pluto.huji.ac.il/~alexg/

Benny Moldovanu

University of Bonn - Chair of Economic Theory II ( email )

Lennestrasse 37
53113 Bonn
Germany
+49 228 736395 (Phone)
+49 228 737940 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Philipp Strack

Yale, Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

No contact information is available for Mengxi Zhang

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