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This paper studies the problem of random assignment with fractional endowments. Fractional endowments complicate matters because the assignment has to make an agent weakly better off than his endowment. I first formulate an exchange economy that resembles the random assignment problem and prove the existence of competitive equilibrium in this economy. I then propose a pseudo‐market mechanism for the random assignment problem that is based on the competitive equilibrium. This mechanism is individually rational, Pareto optimal and justified envy‐free but not incentive compatible.