The standard method for computing the equilibrium strategies of asymmetric first-price auctions is the backward-shooting method. In this study we show that the backward-shooting method is inherently unstable, and that this instability cannot be eliminated by changing the numerical methodology of...

We study all-pay auctions with multiple prizes. The players have the same value for all the certain prizes except for one uncertain prize for which each player has a private value. We characterize the equilibrium strategy and show that, independent of the ranking of the uncertain prize, if the...