Competitive Equilibrium in the Random Assignment Problem

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.