Protocol to identify zone of potential agreement without revealing reservation prices and having to trust third parties? A wants to buy a company from B. Before A and B enter negotiations, they want to make sure that there actually is a zone of potential agreement. Obviously, they don't want to communicate their reservation prices to the other party (A only buys for less than 100m, B only sells for at least 90m). So they both communicate their reservation price to a trusted mediator who then tells them whether or not negotiations makes sense.

Is there a protocol that A and B can use to find out the same thing without having to trust the other and any third parties?
Is there a protocol that A and B can use to find out the same thing
  without having to trust the other and any third parties?


There is. Even more than one.
Your problem actually is equivalent to Yao's Millionaire's Problem.
You have two numbers which two parties want to keep secret and you want both parties to find out whether the one is larger than the other, i.e. compare $a\geq b$ with $a$ being the maximal price willing to be paid by A and $b$ being the least price for which B would sell.

The secure multiparty protocols (credit goes to Ricky for pointing that out) to solve this are various. Because they aren't easy and it's better if you get them from source I'll quickly name three (better protocol suggestions are welcomed):


"Protocols for secure computation" by Yao
"Some Efficient Solutions to Yao’s Millionaire Problem" by Kumar and Gupta
"An Efficient Protocol for Yao's Millionaire's Problem by Ioannidis and Grama