You are also very wrong on hosting, @TDizzle.
1 player hosts the game from their PC/Console and everyone is connected to it. The player with the lowest ping is always is the host.
@TrickshotMcgee was close, but the monster is not always the host. In competitive matches the monster is the host, but not always in pubs. 1/5 players has a chance of hosting there. Otherwise, in pub the host would always be changing if 2 people wanted monster.
TRS does not have private servers that they use to run Evolve multiplayer, because having 5 players on 1 server is a complete waste of hardware and money, especially if the game engine is resource intensive. You would need a PC with minimal specs just to run 1 game with 5 players on it and this is a complete waste. Larger games like BF and CoD are able to host these servers on private servers because 20 or so players are connected to a server, not 5.
The only server TRS would need is a connection server, where players wait in que to find games, but I’m not a networking wizard.