Fairness and efficiency for probabilistic allocations with endowments

We propose to use endowments as a policy instrument in market design. Endowments give agents the right to enjoy certain resources. For example in school choice, one can ensure that low-income families have a shot at high-quality schools by endowing them with a chance of admission. We introduce two new criteria in resource allocation problems with endowments. The first adapts the notion of justified envy to a model with endowments, while the second is based on market equilibrium. Using either criteria, we show that fairness (understood as the absence of justified envy, or as a market outcome) can be obtained together with efficiency and individual rationality.