So in our industry what do people really mean, or think they mean when they ask "Hey. Does that support peer to peer?" Here are a couple of definitions and more clear terminology that I prefer. Maybe I can find some sources to back me up. BTW, I'm thinking of small-scale online today. Although many/most of my architectural biases apply here as well. (Other than whether the server is hosted or not).
Academically speaking, peer-to-peer is a communication topology that, in general, indicates that clients or players communicate directly with each other. Like peer-to-peer file sharing. It is used in contrast with the client-server topology where each client has a single connection to the server, and any interaction between clients is performed by means of the server. One benefit of the peer to peer topology is that data can move between clients with one hop of latency instead of two. One benefit of client-server is that each client can be presented the same data in the same order (deterministically).
However, many people are less concerned with whether two clients communicate directly, but instead use the term peer-to-peer to indicate they desire other features:
- There is no part of the game hosted in a central location like a data center. Note that central-server or authoritative-server is not the same thing as hosted-server.
- There is no stand-alone server that needs to be stood up ahead of time, possibly occupying another piece of hardware. When the player starts their client, the multiplayer game is automatically ready to go. There is no separate server process consuming extra resources on one of the user's machine.
- There is no single point of failure in the distributed system. If the master (usually the first player to start) were to drop out of the game, there is no reason for the remaining players to go through matchmaking again.
So even if you have some of the three problems above, you don't have to jump to the conclusion that client-server is therefore not approprite. And given how much easier it is to get a system running that assumes there is a single authoritative server, I'd recommend you look into it, and prove (ie. measure) whether you have an intractible problem with client server.
In the mean time, I'm going to continue to be skeptical when folks say "I need peer-to-peer". My question will be "what feature of peer-to-peer do you think you need?". My "favorite" topology for small scale non-hosted multiplayer is what I call "peered-server" to contrast it to hosted-server. Client server communication topology, single authoritative simulator, no central persistent hosted server process (other than a match maker, which is not the same thing as a simulator).
Really, the thing to keep in mind is that the process communication topology does not have to equate to the network communication topology. It could be a little more efficient if they match, but could be a lot harder to get your project finished.