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Stochastic uncertainty can cause coordination problems that may hinder mutually beneficial cooperation. We propose a mechanism of ex-post voluntary transfers designed to circumvent these coordination problems and ask whether it can increase efficiency. To test this transfer mechanism, we implement a controlled laboratory experiment based on a repeated Ultimatum Game with a stochastic endowment. Contrary to our hypothesis, we find that allowing voluntary transfers does not lead to an efficiency increase. We suggest and analyze two major reasons for this failure: first, stochastic uncertainty forces proposers intending to cooperate to accept high strategic uncertainty, which many proposers avoid; second, many responders behave only incompletely conditionally cooperatively, which hinders cooperation in future periods.