Mechanism design studies situations where a set of agents each hold private information about their preferences over different outcomes. The designer chooses a center that receives claims about such preferences, selects and enforces an outcome, and optionally collects payments. The classical approach is to impose incentive compatibility, ensuring that agents truthfully report their preferences in strategic equilibrium. Subject to this constraint, the goal is to identify a mechanism, i.e., a way of choosing an outcome and payments based on agents’ reports, that optimizes a given design objective like social welfare, revenue, or some notion of fairness.
There are, however, significant challenges associated with this classical approach. First of all, it can be analytically cumbersome to derive optimal mechanisms for domains that are “multi-dimensional” in the sense that each agent’s private information is described through more than a single number, and few results are known in this case.111One example of a multi-dimensional domain is a combinatorial auction, where an agent’s preferences are described by a numerical value for each of several different bundles of items. Second, incentive compatibility can be costly, in that adopting it as a hard constraint can preclude mechanisms with useful economic properties. For example, imposing the strongest form of incentive compatibility, truthfulness in a dominant strategy equilibrium or strategyproofness, necessarily leads to poor revenue, vulnerability to collusion, and vulnerability to false-name bidding in combinatorial auctions where valuations exhibit complementarities among items (missing[missing], missing)