Complexity of Mechanism Design

The aggregation of conflicting preferences is a central problem in multiagent systems. The key difficulty is that the agents may report their preferences insincerely. Mechanism de­ sign is the art of designing the rules of the game so that the agents are motivated to re­ port their preferences truthfully and a (so­ cially) desirable outcome is chosen. We pro­ pose an approach where a mechanism is au­ tomatically created for the preference ag­ gregation setting at hand. This has sev­ eral advantages, but the downside is that the mechanism design optimization problem needs to be solved anew each time. Focus­ ing on settings where side payments are not possible, we show that the mechanism design problem is N ?-complete for deterministic mechanisms. This holds both for dominant­ strategy implementation and for Bayes-Nash implementation. We then show that if we al­ low randomized mechanisms, the mechanism design problem becomes tractable. In other words, the coordinator can tackle the compu­ tational complexity introduced by its uncer­ tainty about the agents' preferences by mak­ ing the agents face additional uncertainty. This comes at no loss, and in some cases at a gain, in the (social) objective.