Optimal auctions with endogenous budgets

- We study standard IPV auctions when bidders endogenously determine their budgets.
- Prior to bidding, bidders decide how much money to borrow. Borrowing is costly.
- We obtain a revenue ranking of standard auctions: all-pay>first-price> second-price.
- The optimal auction is an all-pay auction with suitably chosen reserve price.

We study the benchmark independent private value auction setting when bidders have endogenously determined budgets. Before bidding, a bidder decides how much money she will borrow. Bidders incur a cost to borrowing. We show that bidders are indifferent between participating in a first-price, second-price and all-pay auction. The all-pay auction gives higher revenue than the first-price auction, which gives higher revenue than the second price auction. In addition, when the distribution of values satisfies the monotone hazard rate condition, the revenue maximizing auction is implemented by an all-pay auction with a suitably chosen reserve price.