Fairness and Efficiency for Probabilistic Allocations with Endowments

Abstract

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. Common policy objectives, such as walkzone or sibling placement can be achieved through endowments (arguably more transparently than via priorities). 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) can be obtained together with efficiency and individual rationality.