Welfare maximizing contest success functions when the planner cannot commit

We analyze how a contest organizer chooses optimally the winner when the contestants' efforts are already exerted and commitment to the use of a given contest success function is not possible. We define the notion of rationalizability in mixed-strategies to capture such a situation. Our approach allows to derive different contest success functions depending on the aims and attitudes of the decider. We derive contest success functions which are closely related to commonly used functions providing new support for them. By taking into account social welfare considerations our approach bridges the contest literature and the recent literature on political economy.