Going into a negotiation, the party at the other end of the table is probably well aware that you’re the boss. This particular situation changes the entire strategical negotiation outlook. Your meeting partners will push and haggle until they reach the desired outcome. Even though nothing prevents the boss from sleeping on it, the dynamic is changed either way.
If you aren’t the boss, your meeting partner(s) know that you don’t have clearance to give the go-ahead either way. They’ll assume that you’ll have to discuss with your superiors. In that case, they would try to cater to your needs as much as possible, hoping you will sell their story for them, internally, the best way you can.
Even as the actual boss or CEO, it can be smart to downplay your role, even obfuscate it. Depending on your company’s corporate governance and structure, there might be a board of directors and even a board of advisers in place. Let your meeting partners know, in due time, that the process for taking this particular decision is designed in such a way that it has to be approved by your board. It makes controlling the dynamic easier.
As the boss, it pays not to be the boss every once in a while.