Two Birds with One Stone: Fairness and Welfare via Transfers

Vishnu V. Narayan, Mashbat Suzuki, Adrian Vetta

Abstract: We study the question of dividing a collection of indivisible items amongst a set of agents. The main objective of research in the area is to achieve one of two goals: fairness or efficiency. On the fairness side, envy-freeness is the central fairness criterion in economics, but envy-free allocations typically do not exist when the items are indivisible. A recent line of research shows that envy-freeness can be achieved if a small quantity of a homogeneous divisible item (money) is introduced into the system, or equivalently, if transfer payments are allowed between the agents. A natural question to explore, then, is whether transfer payments can be used to provide high welfare in addition to envy-freeness, and if so, how much money is needed to be transferred.