Auctions with Financial Externalities

We study sealed-bid auctions with financial externalities, i.e., auctions in which losers’ utilities depend on how much the winner pays. In the unique symmetric equilibrium of the first-price sealed-bid auction (FPSB), larger financial externalities result in lower bids and in a lower expected revenue. The unique symmetric equilibrium of the second-price sealed-bid auction (SPSB) reveals ambiguous effects. We further show that a resale market does not have an effect on the equilibrium bids and that FPSB yields a lower expected revenue than SPSB. With a reserve price, we find an equilibrium for FPSB that involves pooling at the reserve price. For SPSB we derive a necessary and sufficient condition for the existence of a weakly separating equilibrium, and give an expression for the equilibrium.