  We consider two-player contests with the possibility of ties and study the
effect of different tie-breaking rules on effort. For ratio-form and
difference-form contests that admit pure-strategy Nash equilibrium, we find
that the effort of both players is monotone decreasing in the probability that
ties are broken in favor of the stronger player. Thus, the effort-maximizing
tie-breaking rule commits to breaking ties in favor of the weaker agent. With
symmetric agents, we find that the equilibrium is generally symmetric and
independent of the tie-breaking rule. We also study the design of random
tie-breaking rules that are ex-ante fair and identify sufficient conditions
under which breaking ties before the contest actually leads to greater expected
effort than the more commonly observed practice of breaking ties after the
contest.
