Three-player sequential contests with asymmetric valuations

Abstract

We compare the total effort of simultaneous versus (partially and completely) sequential contests with three players competing for asymmetric valuations. We show that the total effort is always maximized by the fully sequential contest, where the strongest player moves first, the second, strongest second, and the weakest third. On the other hand, the total effort is minimized when the players move in the opposite direction (weakest first, strongest last), but the optimal contest may be simultaneous, have a single follower, or be fully sequential.