Robert Wilson criticizes applied game theory's reliance on common-knowledge assumptions. In reaction to Wilson's critique, the recent literature of mechanism design has adopted the goal of finding detail-free mechanisms in order to eliminate this reliance. In practice this has meant restricting attention to simple mechanisms such as dominant-strategy mechanisms. However, there has been little theoretical foundation for this approach. In particular it is not clear the search for an optimal mechanism that does not rely on common-knowledge assumption would lead to simpler mechanisms rather than more complicated ones. This paper tries to fill the void. In the context of an expected revenue maximizing auctioneer, we investigate some foundations for using simple, dominant-strategy auctions.

Many refinements of Nash equilibrium yield solution correspondences that do not have closed graph in the space of payoffs or information. This has significance for implementation theory, especially under complete information. If a planner is concerned that all equilibria of his mechanism yield a desired outcome, and entertains the possibility that players may have even the slightest uncertainty about payoffs, then the planner should insist on a solution concept with closed graph. We show that this requirement entails substantial restrictions on the set of implementable social choice rules. In particular, when preferences are strict (or more generally, hedonic), while almost any social choice function can be implemented in undominated Nash equilibrium, only monotonic social choice functions can be implemented in the closure of the undominated Nash correspondence.