So, I have a few board games and card games that I've played and/or received recently and want to write about them, but I realized that I never really set up a framework for evaluating the quality of interaction, not just between the player and the system, but how the system engenders play between players. Multiplayer, insofar as games are concerned is a broad field and encompasses a number of different modes of play.
Competition, Cooperation, & Everything In-Between
One distinction that needs to be made is between cooperative and competitive play. Many games have one or the other, but many games also possess a combination of both. An example of purely cooperative play would be where a group of players work together to win against the game. One example would be a typical pen and paper roleplaying game like Dungeons and Dragons, where a group of players are largely working together to surmount obstacles in a story, weaved by the dungeonmaster. The dungeonmaster's role isn't competitive because she or he doesn't "win" if all the character's die. It's more of a very hands-on facilitator, like the role of the narrator in a game of Mafia. Likewise, a totally competitive game would be like a game of singles tennis, where two players test each other's physical skill against each other.
Team-based competitive play is the obvious example of cooperative and competitive interaction, like in the children's outdoor game, Capture the Flag. There are also more interesting cooperative/competitive hybrids, such as the dynamic found in The Legend of Zelda: The Four Swords, where players have to work together to complete dungeons, but each are ranked individually by score and so there's a tension between helping each other in order to win together and trying to outdo each other in order for individual glory. On the flipside of the coin, many board and card games, like Monopoly, encourage trading and cooperation but with the idea that eventually only one person will win, leaving alliances fragile and temporary and trade being a measure of who is really getting the better deal when working together.
There Is Art in Interaction
Any actor is aware that the creation of the artifice between two actors is art in itself, an expression between two role-players colliding in a single work. While I'm not necessarily focused on gaming-as-art (although it certainly can be, has been and will continue to be), that quality that emerges between two players of a game, an exchange between the players, when done well, can be moving, pleasing, and possibly enthralling. As such, when evaluating multiplayer games, I think it's somewhat important to focus on the quality of the interaction. If it's merely trying to top a high score on a leaderboard, like on Bejeweled Blitz for Facebook or topping distances in a hammer throw on the track and field sport, I don't really want to consider that any sort of actual multiplayer, but rather, social single-player gaming as there are no mechanics in the game that demand some interface between players.
I suppose, then, when a game's primary mode is multiplayer, I will have to consider the depth of the interaction. Different games have different degrees of multiplayer. For example, in the card game "War" (one of my most reviled games), the two players interact and are competing, but the decks are ultimately stacked and the players are merely turning over cards, iterating a routine and I would consider it poor multiplayer. I feel like good multiplayer keeps you engaged with the other player(s), whether indirectly or directly and the mechanics of the game force you to need to interact with them. So, for that reason, while I find multiplayer battle Tetris to be a lot of fun, its multiplayer aspect is a little limited since merely excelling at playing regular Tetris is what sends lines to your opponent. Super Puzzle Fighter II improves on this regard by providing mechanics to reduce an "attack" by the other player and the game isn't built on playing solo, but rather wiping out an opponent. Both games force you to play better solo because the other player adds a ticking time bomb to your solo game, but Puzzle Fighter requires that you be aware of what your opponent is doing more. Both might be fun, but Puzzle Fighter II has deeper multiplayer.
And, I guess that's how I'm going to be looking at multiplayer aspects of games, whether the game is both single and multiplayer or exclusively multiplayer. I'm not going to say that a game is better or worse by having shallow multiplayer or deep multiplayer--per se. I don't think a value attribution need apply, except insofar as how well the multiplayer succeeds in engaging the participants and how balanced it is. After all, multiplayer gaming is about sharing an entertaining experience--if the game has multiplayer hooks that force players to interact at deep levels, but is otherwise boring, it would be a failure as a game.