In production economies with unequal labor skills, we study axiomatic characterizations of Pareto subsolutions which are implementable by sharing mechanisms in Nash, strong Nash, and subgame perfect equilibria. The sharing mechanism allows agents to work freely and distributes the produced output to the agents, according to the profile of labor hours and the information on demands, prices, and labor skills. Based on the characterizations, we find that most fair allocation rules, which embody the ethical principles of responsibility and compensation, cannot be implemented when individuals’ labor skills are private information.