Competition for Budget-Constrained Buyers: Exploring All-Pay Auctions

This note pursues two primary objectives. First, we analyze the outcomes of an all-pay auction within a store where buyers with and without financial constraints arrive at varying rates, and where buyer types are private information. Second, we investigate the selection of an auction format (comprising first-price, second-price, and all-pay formats) in a competitive search setting, where sellers try to attract customers. Our results indicate that if the budget constraint is not too restrictive, the all-pay rule emerges as the preferred selling format in the unique symmetric equilibrium. This is thanks to its ability to prompt buyers to submit lower bids, thereby generally avoiding budget constraints, while allowing the seller to collect all bids.