Only if one of the bidders is a competitor or company with a symbiotic relationship to the target will there be the possibility of asymmetric valuations. But even then, an outside bidder knowing that the assets have special value to particular buyers will pay more, knowing that they can be resold to this higher valuing buyer. Let's look at your example. The result is that the winner is cursed. This leads rational bidders to lower their bids - to avoid the winner's curse.
Companies are better off selling to a single buyer identified as the most likely to be interested.
Wisc LR 1147 . U.S. executives of publicly-traded companies sometimes prefer a richer mix of individual shareholders, rather than institutional shareholders, because individuals are thought to be less activist. That is, they may be reluctant to sell in a takeover or to vote against incumbent management in a proxy fight. There are a couple reasons for this. That is, they are mostly intermediaries for individual and institutional clients, but not signficant principals.