Evaluating Assignment without Transfers: A Market Perspective

We show that every (random) assignment/allocation without transfers can be considered as a market outcome with personalized prices and an equal income. One can thus evaluate an assignment by investigating the prices and the induced opportunity sets. When prices are proportional across agents, the assignment is efficient; when prices are common, the assignment is both efficient and envy-free. Moreover, this market perspective reveals a weakness of envy-freeness.