A Multiplayer game of Magic is each a mode of the card game that involves more than two players. The players might be independent opponents or formed into teams.  
Multiplayer variants are not stand alone formats. You don't play Two-Headed Giant on its own, but rather play Two-Headed Giant Standard or Two-Headed Giant Sealed Deck.
Some cards are especially suitable for this kind of group play.      
From the Comprehensive Rules (Hour of Devastation (July 8, 2017))
- 800. General
- 800.1. A multiplayer game is a game that begins with more than two players. This section contains additional optional rules that can be used for multiplayer play.
- 800.2. These rules consist of a series of options that can be added to a multiplayer game and a number of variant styles of multiplayer play. A single game may use multiple options but only one variant.
- 800.3. Many multiplayer Magic tournaments have additional rules not included here, including rules for deck construction. See the most current Magic: The Gathering Tournament Rules for more information. They can be found at WPN.Wizards.com/en/resources/rules-documents.
- 800.4. Unlike two-player games, multiplayer games can continue after one or more players have left the game.
- 800.4a When a player leaves the game, all objects (see rule 109) owned by that player leave the game and any effects which give that player control of any objects or players end. Then, if that player controlled any objects on the stack not represented by cards, those objects cease to exist. Then, if there are any objects still controlled by that player, those objects are exiled. This is not a state-based action. It happens as soon as the player leaves the game. If the player who left the game had priority at the time he or she left, priority passes to the next player in turn order who’s still in the game.
Example: Alex casts Mind Control, an Aura that reads, “You control enchanted creature,” on Bianca’s Assault Griffin. If Alex leaves the game, so does Mind Control, and Assault Griffin reverts to Bianca’s control. If, instead, Bianca leaves the game, so does Assault Griffin, and Mind Control is put into Alex’s graveyard.
Example: Alex casts Act of Treason, which reads, in part, “Gain control of target creature until end of turn,” targeting Bianca’s Runeclaw Bears. If Alex leaves the game, Act of Treason’s change-of-control effect ends and Runeclaw Bears reverts to Bianca’s control.
Example: Alex casts Bribery, which reads, “Search target opponent’s library for a creature card and put that card onto the battlefield under your control. Then that player shuffles his or her library,” targeting Bianca. Alex puts Serra Angel onto the battlefield from Bianca’s library. If Bianca leaves the game, Serra Angel also leaves the game. If, instead, Alex leaves the game, Serra Angel is exiled.
Example: Alex controls Genesis Chamber, which reads, “Whenever a nontoken creature enters the battlefield, if Genesis Chamber is untapped, that creature’s controller creates a 1/1 colorless Myr artifact creature token.” If Alex leaves the game, all such Myr tokens that entered the battlefield under Alex’s control leave the game, and all such Myr tokens that entered the battlefield under any other player’s control remain in the game.
- 800.4b If an object would change to the control of a player who has left the game, it doesn’t. If a token would be created under the control of a player who has left the game, no token is created. If an object would be put onto the battlefield or onto the stack under the control of a player who has left the game, that object remains in its current zone. If a player would be controlled by a player who has left the game, he or she isn’t.
- 800.4c If an effect that gives a player still in the game control of an object ends, there is no other effect giving control of that object to another player in the game, and the object entered the battlefield under the control of a player who has left the game, the object is exiled. This is not a state-based action. It happens as soon as the control-changing effect ends.
- 800.4d If an object that would be owned by a player who has left the game would be created in any zone, it isn’t created. If a triggered ability that would be controlled by a player who has left the game would be put onto the stack, it isn’t put on the stack.
Example: Astral Slide is an enchantment that reads, “Whenever a player cycles a card, you may exile target creature. If you do, return that creature to the battlefield under its owner’s control at the beginning of the next end step.” During Alex’s turn, Bianca uses Astral Slide’s ability to exile Alex’s Hypnotic Specter. Before the end of that turn, Bianca leaves the game. At the beginning of the end step, the delayed triggered ability generated by Astral Slide that would return Hypnotic Specter to the battlefield triggers, but it isn’t put on the stack. Hypnotic Specter never returns to the battlefield.
- 800.4e If combat damage would be assigned to a player who has left the game, that damage isn’t assigned.
- 800.4f If an object requires a player who has left the game to make a choice, the controller of the object chooses another player to make that choice. If the original choice was to be made by an opponent of the controller of the object, that player chooses another opponent if possible.
- 800.4g If a rule requires a player who has left the game to make a choice, the next player in turn order makes that choice.
- 800.4h If an effect requires information about a specific player, the effect uses the current information about that player if he or she is still in the game; otherwise, the effect uses the last known information about that player before he or she left the game.
- 800.4i If a player leaves the game during his or her turn, that turn continues to its completion without an active player. If the active player would receive priority, instead the next player in turn order receives priority, or the top object on the stack resolves, or the phase or step ends, whichever is appropriate.
- 800.4j If a player who has left the game would begin a turn, that turn doesn’t begin.
- 800.4k When a player leaves the game, any continuous effects with durations that last until that player’s next turn or until a specific point in that turn will last until that turn would have begun. They neither expire immediately nor last indefinitely.
- 800.4m When a player leaves the game, objects that player owns in the ante zone do not leave the game. This is an exception to rule 800.4a. See rule 407, “Ante.”
- 800.4n In a Planechase game, if the player designated as the planar controller would leave the game, instead the next player in turn order that wouldn’t leave the game becomes the planar controller, then the old planar controller leaves the game. See rule 309.5.
- 800.5. In a multiplayer game, the first time a player takes a mulligan, he or she draws a new hand of as many cards as he or she had before. Subsequent hands decrease by one card as normal.
- 800.6. In a multiplayer game other than a Two-Headed Giant game, the starting player doesn’t skip the draw step of his or her first turn. In a Two-Headed Giant game, the team who plays first skips the draw step of their first turn. See rule 103.7.
Some Multiplayer archetypes are:
- ↑ Anthony Alongi. (November 26, 2002.) “The Only Hard and Fast Rule”, magicthegathering.com, Wizards of the Coast.
- ↑ Zac Hill. (June 01, 2012.) “Multiplayer Development”, magicthegathering.com, Wizards of the Coast.
- ↑ Anthony Alongi. (September 23, 2003.) “The Hall Monitor Returns”, magicthegathering.com, Wizards of the Coast.
- ↑ Mike McArtor. (October 13, 2014.) “The First Hall”, magicthegathering.com, Wizards of the Coast.
- ↑ Bruce Richard. (October 13, 2014 .) “Welcome to the Multiplayer Hall of Fame!”, magicthegathering.com, Wizards of the Coast.
- ↑ MULTIPLAYER HALL OF FAME
- ↑ Mark Rosewater. (October 13, 2014.) “Team Building”, magicthegathering.com, Wizards of the Coast.
- ↑ Gavin Verhey. (January 26, 2016.) “Five Steps to Building a Multiplayer Magic Deck”, magicthegathering.com, Wizards of the Coast.