It's important when entering any negotiation to make sure that your counterpart has the decision-making power to conclude your discussions. According to a study by The American Management Association the 5th most common negotiation tactic is claiming "Lack of Authority" at a critical point in the process - which was reported by 11% of respondents.
The other party is using this 'no authority' tactic to drain your energy and willpower. They are simply conducting reconnaissance for the "main event" - which will be a subsequent negotiation between the "higher-ups". Don't fall for it.
If at any point the person on the other side of the table reveals that they are not authorised to make a deal, then refuse to continue with discussions until you’re talking to the right person. Talking to anyone else is a waste of your time and energy.
So, ask up front who the final decision maker is, and don’t talk to anyone else.