A Theory of Auctions with Endogenous Valuations

We derive the symmetric, revenue-maximizing allocation of several units among agents who take costly actions that influence their values. The problem is equivalent to a reduced-form model where have nonexpected utility. uniform-price auction and discriminatory pay-your-bid with reserve prices react both demand supply constitute optimal mechanisms. also identify condition under which overall mechanism indeed symmetric illustrate structure asymmetric when fails. main tool in our analysis an integral inequality based on Fan Lorentz (1954).