A New Solution to the Random Assignment Problem with Private Endowment

This paper proposes a new mechanism to solve random assignment problems in which some agents have private endowments. The new mechanism generalizes the Probabilistic Serial mechanism by letting agents benefit from the popularity of their private endowments, which is summarized by the idea of “you request my house I get your speed”. Interestingly, the same idea can also be used to deal with indifferent preferences in Probabilistic Serial and our generalization. Our method is straightforward to understand and easy to implement compared with the previous method of solving maximum network flow problems in the literature.