GDC week = time to post all my rambly crap.
I'm interested in the difference between single- and multi-player games.
There's a lot to be said for multiplayer games: human players add a lot to the game. Even if they are not permitted to create content, they are content. An easy example is the Street Fighter series: these kinds of fighting games only really come alive when there is another human playing the other fighter.
For a long time, games have been primarily about competitive multiplayer. Some games are marginally cooperative, in that they have two teams competing, but fully cooperative games are very rare. These days, they are becoming a bit more common with games like Shadows Over Camelot (board) and coop story mode in Halo-like games.
Either way you slice it, competitive, cooperative, or both, the other humans add a lot to the game.
But they also take a lot away from the game, a point that is often missed.
An interesting note is that cooperative and competitive team size remains the same. A fully cooperative game has a "maximum player count" of almost precisely half the competitive-teams maximum player count in games using the same basic mechanics.
A game dedicated to one player makes that player the focus of the entire universe. That player doesn't need to worry about going at the right speed or doing the right things: he can just play around without any such concerns.
As you add players, the game allows each of them to play on a more-or-less even footing. Basically, you have to play with the other player, rather than just doing whatever you want. Each player adds more limits.
For example, a two-player fighting game: you and another person fight... to the death!
A four-player fighting game like Smash Brothers is the same on the surface, but it's actually a lot less free: each player has to watch every other player and make sure nobody gets a sneak attack on them. Their choices are limited by the existence of the other players. Some four-player games are tag-battles: two in, two out at any given time. This simply reduces the game to a two-player hotseat, meaning the complexity of a two player game, but you spend half your time not doing anything.
Players really can't track too many variables at a time, so as you add more than four players, you have to start figuring out how to reduce the chaos. Games like Quake allow for large deathmatch games of six or eight players, but the levels are designed to keep you from encountering more than a few other players at any given time.
This doesn't completely write out the complexity of having a lot more players: someone is in the lead, better watch for them. Someone just got the quad-damage, better watch out for him... global multiplayer concerns still exist. But you don't have to worry about all the players simultaneously. This does reduce the player's agency: the player's access to information is brutally limited.
These global multiplayer concerns get too difficult shortly thereafter. With ten or twelve players, hunting down the man in the lead is a herculean task, and the random chaos will frequently lead to wild, crowded encounters that players can only "track" by lobbing explosives towards the general area.
One easy method to reduce complexity is to reduce the number of enemies a player has. By making the game team-based, half the players are allies and half the players are enemies. This allows for much greater cohesion and predictability, and easily allows for games of up to twenty or thirty players, if you have decent training. Of course, this further reduces the player's agency, as now he plays a specific role as a tiny cog in a large team.
Even this has its limits. As you pass thirty, the teams are so large that any given player will have no real effect on the state of the game. Because the teams are so large and most players have to have an even amount of power, you can't really change the tide of battle much.
At this point, games usually break down into social events. Basically, the designers say "well, we've reduced the power of the player to pretty close to nothing, so I guess there's no point to truly competitive play..."
But, of course, competitive play is popular, so there's always a few outs. Arenas, PvP, etc. You will find that these subgames follow the same pattern listed above.
Actually, you will find that a social game breaks up fuzzily and follows the patterns listed above even in non-competitive areas. For example, cohesive guilds tend to max out at thirty players. Most groups on-the-fly tend to be four or five people, and larger groups tend to have a chain of command that splits them into wings of three or four...
Also to be considered is unfairness. Not all players want the same thing: many people are happy being the star-bit-collector in Super Mario Galaxy. Many people are happy crafting and buying/selling, rather than the "primary" game of killing shit. But this doesn't change the fundamental nature of multiplayerness. It simply changes the texture. If Mario's world was much more complicated, more than four star-bit-collectors would be chaotic and cripplingly confused. However, you can consider the star-bit-collectors to be on a different "team" than Mario (noncompetitive teams...), so the star-bit-collectors could number three or four and the Marios could number three or four without "overloading" the players too much.
"Unfair" (more accurately, "uneven") situations are another method of splitting players into groups to shrink the complexity of their interactions. But, as I said, this doesn't change the basic situation.
I would personally like to see a massively multiplayer game that leaves the player with power over the universe... but uses some of these other techniques to control player interactions. Maybe even some techniques not listed here.
There's a lot you can do to reduce the "chaos" of multiple players. Reducing player power to zero isn't really my favorite.
Spore promised an interesting variant, where each player has their own universe in which they have huge amounts of control. But each player "leaks" into other universes, hopefully granting a portion of the power of multiplayer. I tend to think that the social aspect is probably the most important aspect of multiplayer, and this system had no social aspect.
Now, though, they've expanded the Spore backbone to include a lot of social elements like card trading and so forth. I think it will probably be done very poorly, but it's an interesting attempt to solve the multiplayer "problem" of balancing chaos with power.
(By the way, player power is being measured in terms of ability to affect the global game state. A player's ability to blow away a monster has nothing to do with that, since the monster respawns a few seconds later and nothing changes.)