Working Paper, Brown University, Department of Economics 2016-6
Models of choice where agents see others as less sophisticated than themselves have significantly different, sometimes more accurate, predictions in games than does Nash equilibrium. When it comes to mechanism design, however, they turn out to have surprisingly similar implications. This paper provides tight necessary and sufficient conditions for implementation with bounded depth of reasoning, discussing the role and implications of different behavioral anchors. The central condition slightly strenghthens standard incentive constraints, and we term it strict-if-responsive Bayesian incentive compatibility (SIRBIC).