The Perfesser has a fascinating, pretty nontechnical discussion of the business judgment rule in corporation law up on his website (it should be an education for authors who constantly wonder why the publishing business seems so conservative). I would like to point out one unstated assumption, though. It is not necessarily a bad assumption; but because it is unstated, it should be at least acknowledged.
There is a commonplace assumption that the Supreme Court held, in the late 19th century, that "corporations are persons" for purposes of the right to sue and be sued. Well, it didn't; the statement in question was added by the Reporter of Decisions in the syllabus, and appears nowhere in the decision itself. Santa Clara Cty v. Southern Pac. R. Co., 118 U.S. 394 (1886) (unfortunately, the publicly available free versions do not include the syllabus). The reporter states that during oral argument the question was foreclosed by the justices; but that is not consistent with then-current practice. It is possible; it is internally consistent with the reasoning in the opinion; it might even make sense; but it is not the law.
The assumption to which I am referring is the dichotomy between the Corporation and corporate operations. In the strictest sense, Corporations are not persons, because they cannot make decisions for themselves. At most, they are infants, whose every decision must be made by a parent. Professor Bainbridge's essay is an attempt to define just who those parents are. It is underinclusive, as all purely economic analysis of corporations must be. For example, it does not concern itself with corporate operations that are outside the bounds set by law, such as OSHA or environmental regulations. Neither does it concern itself with the symbiosis of the corporation with its communities; just as "no man is an island," no corporation is isolated from its community. Not even Willy Wonka's chocolate factory is truly isolated, even though all but one of his employees was an Oompa-Loompa; people were driving the trucks, collecting the taxes, building franchise shops, etc. Conversely, there is no reason for Mobil Oil to sponsor Masterpiece Theater on PBS except insofar as it wants to take advantage of that symbiosis. I do not believe that this symbiotic relationship, except in extreme circumstances, should be a controlling factor. However, the purely economic models ignore it completely; and for that reason, arguing over whether the directors or the shareholders are the "brain" of the corporation is an incomplete inquiry doomed to come up with an incomplete answer.