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Competitive Equilibrium in the Random Assignment Problem

Le, Phuong (2013): Competitive Equilibrium in the Random Assignment Problem.

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This paper studies the problem of random assignment with fractional endowments. In the random assignment problem, a number of objects has to be assigned to a number of agents. Though the objects are indivisible, an assignment can be probabilistic: it can give an agent some probability of getting an object. Fractional endowments complicate the matter 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.

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