  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.
