A Theory of Auctions with Endogenous Valuations

52 Pages Posted: 22 Oct 2018

See all articles by Benny Moldovanu

Benny Moldovanu

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

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Date Written: October 2018

Abstract

We study the revenue maximizing allocation of m units among n symmetric agents that have unit demand and convex preferences over the probability of receiving an object. 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

Moldovanu, Benny, A Theory of Auctions with Endogenous Valuations (October 2018). CEPR Discussion Paper No. DP13259, Available at SSRN: https://ssrn.com/abstract=3270937

Benny Moldovanu (Contact Author)

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

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