We use experiments to compare dynamic and static wars of attrition (i.e. second-price all-pay auctions) and first-price all-pay auctions. Many other studies find overbidding in first-price all-pay auctions. We can replicate this property. In wars of attrition, however, we find systematic underbidding. We study bids and revenue in different experimental frames and matching procedures and draw a link to the literature on stepwise linear bidding functions.