We present a survey of the emerging literature on the design of matching markets. We survey the articles on discrete resource allocation problems, their solutions, and their applications in three related domains. The first domain gives the theoretical background regarding the basic models,...

We evaluate the goal of maximizing the number of individually rational assignments. We show that it implies incentive, fairness, and implementation impossibilities. Despite that, we present two classes of mechanisms that maximize assignments. The first are Pareto efficient, and undominated - in...

Shortages in organs for transplantation have resulted in a renewed interest in designing incentive policies to promote organ supply. The donor‐priority rule, which grants priority for transplantation based on deceased organ donor registration status, has proven to be effective in both theory...

Goods and services---public housing, medical appointments, schools---are often allocated to individuals who rank them similarly but differ in their preference intensities. We characterize optimal allocation rules when individual preferences are known and when they are not. Several insights...

Many scarce public resources are allocated at below-market-clearing prices, and sometimes for free. Such "non-market" mechanisms necessarily sacrifice some surplus, yet they can potentially improve equity. In this paper, we develop a model of mechanism design with redistributive concerns. Agents...

We study a large market model of dynamic matching with no monetary transfers and a continuum of agents who have to be assigned items at each date. When the social planner can only elicit ordinal agents' preferences, we prove that under a mild regularity assumption, incentive compatible and...

The allocation and exchange of discrete resources, such as transplant organs, pub- lic housing, dormitory rooms, and many other resources for which agents have single-unit demand, is often conducted via direct mechanisms without monetary transfers. Incentive compatibility and ef?ciency are...

In 56 developing and developed countries, blood component donations by volunteer non-remunerated donors can only meet less than 50% of the demand. In these countries, blood banks rely heavily on replacement donor programs that provide blood to patients in return for donations made by their close...

In the allocation of indivisible objects under weak priorities, a common practice is to break the ties using a lottery and randomize over deterministic mechanisms. Such randomizations usually lead to unfairness and inefficiency ex-ante. We propose and study the concept of ex-ante fairness for...