Every Friday, I'll toss an idea or two with regards to tabletop RPGs.
This isn't limited to RPGs but can be applied to games in general. What's the minimum/maximum players and how does the numbers of players change the group dynamics?
D&D for example assumes there's five players and one GM. Adding or subtracting one player more or less keeps the design goals intact but anything beyond that alters the game significantly (which isn't to say it can't be resolved but there's some tinkering involved). An eight-player game for example might make combats last quite a long time and "group initiative" (the player's turn vs. the GM's turn) becomes a detriment as the 8 characters on one side might gang up on one monster and vice versa (8 monsters ganging up on a single PC). It's also difficult to devote time tackling individual storylines in an eight-player game because it could bog down and leave 7 players waiting for the other person to resolve their plotline.
Some GMs are turned off at running a two-player D&D game (mainly it's a factor of time/effort efficiency--that is the hours of prep rewarding only two players when it could easily have been four or five) and again it's a different party dynamic. When it comes to combat, players have to carefully pick their roles. As for roleplaying, there's room here for the party to "split apart" and delve into more complex storylines as the GM only has to divide his attention to two players.
A better example would be other sorts of games. Mafia/Werewolf for example is a great party game but it's not infinitely scalable. I don't think it's possible to run it for a 30-person group for example. On the other end of the spectrum, it can resolve pretty quickly if you're just running it for five people or so.
When applied to RTS games, the number of players actually changes the type of game you're playing. Let's take my experiences with Warcraft III. One on one is the assumed default and you're faced to changed tactics as it becomes a 1 vs. 1 vs. 1 game. You know for certain one player will eventually have to sit it out as they become the first person eliminated. Launching a full attack on one player also leaves you very vulnerable and the game can slow down as each player carefully plays the cat-and-mouse game, waiting for one player to take action and take advantage of that opportunity. In a 2 vs. 2 game, one player's skill can make up for your partner's lack of talent (and it's possible to win a 2 vs. 1 game if you play your cards right). In a 5 vs. 5 game, I've discovered that the individual player's skill level matters less and cooperation and teamwork plays a bigger role. No matter how good you are, 5 opponents at your front door will lead to a massacre.
One element of RPGs however is that they don't tend to tell you on the cover the minimum/maximum players required for the game. It's a stark contrast to board games which mention it outright in the box. Again, that's not to say RPG games aren't scalable, but I'd like to think the designers have an ideal number in mind when designing such a game. Or at the very least, the number of players changes how one interacts with the rest of the group.