A Theory of Auctions with Endogenous Valuations

49 Pages Posted: 9 Jan 2018 Last revised: 13 Feb 2018

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

University of California, Berkeley - Department of Economics

Date Written: February 5, 2018

Abstract

We study the revenue maximizing allocation of m units among n symmetric agents with unit demand that have convex preferences over the probability of receiving an object. We show that such preferences are naturally induced by a game where the agents take costly actions that affect their values before participating in the mechanism.

Both the uniform m 1 price auction and the discriminatory pay-your-bid auction with reserve prices constitute symmetric revenue maximizing mechanisms. Contrasting the case with linear preferences, the optimal reserve price reacts to both demand and supply, i.e., it depends both on the number of objects m and on number of agents n. The main tool in our analysis is an integral inequality involving majorization, super-modularity and convexity due to Fan and Lorentz (1954).

Suggested Citation

Gershkov, Alex and Moldovanu, Benny and Strack, Philipp, A Theory of Auctions with Endogenous Valuations (February 5, 2018). Available at SSRN: https://ssrn.com/abstract=3097217 or http://dx.doi.org/10.2139/ssrn.3097217

Alex Gershkov

Hebrew University of Jerusalem ( email )

Mount Scopus
Jerusalem, IL 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 (Contact Author)

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

HOME PAGE: http://philippstrack.com

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