Incentive compatible allocation and exchange of discrete resources

Allocation and exchange of many discrete resources – such as kidneys or school seats – is conducted via direct mechanisms without monetary transfers. A primary concern in designing such mechanisms is the coordinated strategic behavior of market participants and its impact on resulting allocations. To assess the impact of this implementation constraint, we construct the full class of group dominant-strategy incentive compatible and Pareto efficient mechanisms. We call these mechanisms “Trading Cycles.” This class contains new mechanisms as well as such previously studied mechanisms as top trading cycles, serial dictatorships, and hierarchical exchange. In some problems, the new trading-cycles mechanisms perform better than all previously known mechanisms. Just as importantly, knowing that all group incentive-compatible and efficient mechanisms can be implemented as trading cycles allows us to determine easily which efficient outcomes can and cannot be achieved in a group incentive-compatible way.