Effort maximization in contests under balance constraints

We study all-pay contests with complete information and two heterogeneous contestants who compete for a single prize. We combine two common designer's goals which are combined especially in sports contests; effort maximization and competitive balance. We focus on two cases when the designer's utility is either continuous or discontinuous in the contestants' efforts. We show that a maximum effort constraint is always efficient for increasing the designer's utility, namely, effort maximization under competitive balance.