Discussion paper

DP13259 A Theory of Auctions with Endogenous Valuations

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 a ect their values before participating in the mechanism. Both the uni-
form 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).


Moldovanu, B (2018), ‘DP13259 A Theory of Auctions with Endogenous Valuations‘, CEPR Discussion Paper No. 13259. CEPR Press, Paris & London. https://cepr.org/publications/dp13259