In a peer to peer environment, the first one to open up the files becomes the "host". The rest of them should connect using open remote as clients. There are some things to keep in mind when one is using the host copy. Any changes to global fields will change them for the clients the next time they connect. As a strong precaution, nobody should have OS level access to the files.
IMO a dedicated machine that serves the files and acts as the host is the way to go even in a peer to peer scenario.
Agreeing with Mr. Vodka,
You get better response times and lower your risk of problems if your Peer to Peer Host isn't used for anything but hosting the database.
You shoud also really use FileMaker Server (Advanced) to host your databases, instead of FileMaker Pro client. It can schedule backups and other scripts, provides many more simultaneous connections, is *much* more robust and stable, among myriad other features.
If you don't want to invest in your own server hardware and software license, you may want to consider using a professional FileMaker hosting provider, such as ourselves:
We provide the server hardware, FileMaker Server Advanced licenses, upgrades, monitoring, etc. so you don't have to - and the expense is fully deductible as a service vs. having to depreciate hardware/software over a number of years. Feel free to let me know if you have any additional questions either here or off-list to jmay(at)pointinspace.com. Thanks!
Apart from the aforesaid reasons, limitations such as number of connections allowed should also be taken into consideration. FMSA 11 no longer limits the number of FileMaker Pro clients. Connections are limited only by hardwares and OS.