Revenue ranking of optimally biased contests: The case of two players

•The asymmetric two-player Tullock contest has a unique equilibrium for r≤2.•This result completes, in a sense, the analysis of the two-player Tullock contest.•We offer a comprehensive view on the comparative statics of the model.•We also show that the equilibrium set does not depend on the tie-breaking rule.•As an application, we derive a revenue ranking for optimally biased contests.

It is shown that the equilibrium in the asymmetric two-player Tullock contest is unique for parameter values r≤2. This allows proving a revenue ranking result saying that a revenue-maximizing designer capable of biasing the contest always prefers a technology with higher r.