Before revision:  In this work, we study , for the first time, infinite-duration all-pay bidding games , and show that they exhibit the elegant{\em   mathematical properties of their first-price counterparts . This is in stark contrast with reachability games, which are known to be much more complicated under{\em   all-pay bidding than first-price bidding.
After revision:  In this work, we study , for the first time, infinite-duration all-pay bidding games , and show that they exhibit the elegant{\em mathematical properties of their first-price counterparts ; namely, an equivalence with{\em all-pay bidding than first-price bidding.