For a specific number of players

Generally this does not mean the game's impossible to play with less, but it is likely much less enjoyable or makes less sense (missing characters during gameplay who pop up during Plot Events).

Usually noticeable from the fact that AI controls the remaining character, even more so when they aren't controlled by anyone, or outright denying playing with less (requires extra supported controllers to be connected, all to have start pressed, etc.).

This is not for cases where you can have more than the designated number of players, and not for games that are simply for 1 to # players, but those that are designed specifically an unmalleable number of players.

Common-ish for more recent cooperative games where the single player campaign only marginally works without the other players.

In some cases if there's less than the designated number of players, the host controls all excess characters instead of them being evenly spread out to the players.

Other signs:
* There's always something vital for all players instead of just one (as it would be if it wasn't designed for more). Designed for 2? You'll find 2 jeeps or that one jeep has a driver and gunner seat, or 2 mechs, even if you play alone.
... or there's turrets for all players instead of 1 for same direction.
... or playing alone forces you to swap seating in said jeep instead of having mysterious control over both driving and the gun with single character.
* Levels are designed so that the other players can simultaneously use alternative routes, encircling or flanking the coming opposition.
* Stashes for equipment have the new stuff for all players. Find new suit? Everyone gets it.

There may be some aversions from this where one character is selected to do a specific task (e.g. charge in some vehicle rigged with explosives) while the others do something else (prepare for assault after the "diversion"), which blurs the boundary of being designed for more than one.

See also: 3 or more players, cooperative multiplayer

Implied: bots