Office Depot Inc. and OfficeMax set up a competition of the bosses, saying they’ll wait to pick whether either of their chief executive officers will be in charge when the companies merge.

The decision not to decide may lead to management challenges later, said executive recruiters and corporate governance experts who were unable to recall a similar case. The shares of both companies declined Wednesday, with Office Depot dropping 17 percent in the biggest plunge since April 2010.