Finding the right agent

[Anastasiia Greca]

Some people mentioned that when you are buying a house you should get a "Buyer Agent". 
So as I see it:

Seller Agent - negotiation the largest price possible for the house to satisfy his seller needs

Buyer Agent - negotiation the smallest price possible for the house to satisfy his buyer needs
Both types of agent get payed through commission, basically by the seller.
So my question is - why would Buyer agent try to get lower price, if that means he is getting less money? Am I missing something? Maybe I (Buyer) supposed to pay something to my agent? 

Do you have to sign Buyer Broker Agreement? 

And what happens if you cant find the right deal, but your Buyer Broker Agreement time frame is coming to an end? Do you have some penalties or fees you supposed to pay for working with agent?