Before revision:  Under poorman all-pay bidding , in contrast to Richman bidding, deterministic strategies are useful and guarantee a payoff that is only slightly lower than the optimal payoff under first-price poorman bidding. Our proofs are constructive and based on new and significantly simpler constructions for first-price bidding.
After revision:  Under poorman all-pay bidding are more intricate and unexpected than for first-price bidding.