According to the definition set forth by “The Many Faces of Sociability and Social Play in Games”, it is a game where there are three or more participants who can have a direct casual effect on all other participants. There are four main types of multiplayer: co-op, competitive, collaborative and massive-multiplayer. Even single player games nowadays are becoming more and more multiplayer-like due to the sociability in games. A true single player game is played by one person and is never compared to or played with another person. As soon as you add in leader boards or comparisons on completion, the game becomes multiplayer.
Pattern of Co-Op Multiplayer Pattern of Collaborative Multiplayer Pattern of Competitive Multiplayer Pattern of Massive Multiplayer
Competitive - League of Legends
In League of Legends players must help each other to defeat the enemy team. This is very competitive since it is up to your team to not screw up and lose while at the same time you have the potential to lose the game for your team if you mess up as well.
Co-Op - Gears of War 3
Gears of War 3 co-op In Gears of War 3 co-op, you and up to 3 other players play as the 4 characters fighting through the campaign together. You can also change the mode to score points and compete against each other for the most points if you want as well.
Collaborative - Minecraft
Massive Multiplayer - World of Warcraft
World of Warcraft is played by over 7 million people. The game is evenly dispersed from new to advanced players with countless leaderboards, forums and guilds to provide hundreds of ways to compete against or with other players.
Multiplayer is not playing the game with another person on the same screen, as that is a form of Two Player. There are many types of multiplayer but subtle changes, such as in the gears of war co-op, can change it from competitive to collaborative or co-op or vice-versa.
This pattern(s) is industry standard.