Core deviation minimizing auctions

In a stylized environment with complementary products, we study a class of dominant strategy implementable direct mechanisms and focus on the objective of minimizing the expected surplus from core deviations. For this class of mechanisms, we formulate the core deviation minimization problem as a calculus of variations problem and numerically solve it for some interesting special cases. We then compare the core deviation surplus in the optimal auction (CDMA) to that in Vickrey-Clark-Groves mechanism (VCG) and core-selecting auctions (CSAs). We find that the expected surplus from core deviations can be significantly smaller in CDMA than that in both VCG and CSAs.