Foundations of Dominant Strategy Mechanisms

Wilson (1987) criticizes the existing literature of game theory as relying too much on common-knowledge assumptions. In reaction to Wilson's critique, the recent literature of mechanism design has started to employ stronger solution concepts such as dominant strategy incentive compatibility, and restrict attention to simpler mechanisms such as dominant strategy mechanisms. However, there has been little theory behind this approach. In particular, it has not been made clear why employing simpler mechanisms, instead of more complicated ones, is the correct way to address Wilson's critique. This paper aims at filling this void. We propose a potential theory, known as the {\it maxmin} theory, which postulates that a {\it cautious} mechanism designer, facing uncertainty over which (common-knowledge) assumptions are valid and which are not, would indeed rationally choose simpler mechanisms such as dominant strategy mechanisms. In this paper, we summarize our progress in proving this theory, explore other possible theories, and discuss related theoretical questions that will be of interest in other areas