I need to interpret some empirical results telling me that firms (intended as profit-maximising entities) prefer to be controlled (e.g. through interlocking directorships) by smaller and less profitable companies. I couldn't find any piece of literature helping me in this sense. Do you have some advice on that? Any hint would be really appreciated.
I've heard of this phenomenon but not for the reasons you suggest:
The largest corporations tend to have the most interlocks (Table 4). This may occur because the directors of the largest corporations are the most knowledgeable, the most capable, and the most accomplished men available. Other corporations would naturally seek their advice and would rather have them on their board than men of less ability. This may also occur, however, because of factors unrelated to managerial ability. The director of a giant corporation undoubtedly has more personal influence with other companies, with potential investors, and with the government than the common man. Having the director from a large corporation on your board may also lead to profitable business with that corporation.
Dooley, P. C. (1969). The interlocking directorate. American Economic Review 59(3), 314–323