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Excerpted from Beyond Dungeons & Dragons at PAX AUS 2013, we take on the definition of the word "game." Following on from Garfield's "orthogame," we propose "idiogame" for another class of what all fall under the umbrella of "game." If an orthogame is " a competition between two or more players using an agreed-upon set of rules and a method of ranking," then an idiogame is roughly "a series of interesting decisions that produce a personal outcome."
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A competition between two or more players using an agreed-upon set of rules and a method of ranking.
Idiogame:
A game presenting a series of interesting player decisions that produce a personal outcome.
Role Playing Game:
A method of conflict resolution for collaborative storytelling.
Pseudogame:
A game which does not reflect decisions made by players, or does not accept player input of any kind.
How would you describe a cooperative group game, such as Hanabi, where there are a series of individual player decisions which lead towards a group outcome?
Basically, the most important factor is where your utility function comes from - is it derived directly from the rules of the game ("you play to win the game!"), or does it come from your own personal motivations?
For many games it will lie somewhere in between, but the extreme ends of the spectrum are where the terms "orthogame" and "idiogame" are most applicable.
On the whole, though, there is definitely a class of single-player and cooperative games that share a clearly-defined scoring system with the orthogames; absent another term, "puzzle" is probably a good word to use.
However, as we've said before, almost all cooperative games are shit games.
The reasons why are pretty simple, too - a team of players is, in theory, equivalent to a single player, and so cooperative games are essentially single-player games, and competitive games with fixed teams are equivalent to games between individual players.
Non-tabletop games have good reasons for having teams, because there is typically a real-time aspect of coordination and execution, as well as physical limitations; this means there is nontrivial work done by having multiple players as opposed to one.
On the other hand, in a tabletop game these factors aren't there, and so it takes particularly good game design to construct a game where multiple players are not simply redundant.