Optimal equity auction with interdependent valuations?

This study considers a seller using an equity auction to sell an indivisible asset for which bidders have interdependent valuations. First, we introduce bidders' conditional virtual valuations for this setting, and identify sufficient conditions for conditional virtual valuations' monotonicity and singlecrossing property. Then, we characterize the optimal equity mechanism, which is ex post incentive compatible and individually rational. In general symmetric case, English equity auction or two-round sealed bid equity auction with an endogenous take-it-or-leave-it contract can implement the optimal ex post equity auction; in asymmetric case, English auction with an endogenous discriminatory equity contract could be constructed for the implementation of the optimal ex post equity auction under certain conditions.