Reader JV sent me this article about three-way chess, but it looks to me like it would turn into a mess very quickly. The first player to check-mate any other player wins, and any two players can obviously team up on the third very easily.
Does anyone know of any three-player adversarial games that don't turn into two-on-one dogpiles every time? Such a game would have to be inherently asymmetric, such that two players were forced to align against a more-powerful third, or such that the relationships between the players were not commutative (rock vs. paper vs. scissors). I imagine a three-player game would also be more likely to be playable if it were either not turn-based, or at least not based on cyclical turns.