Identify: time travelling game
This sounds like Chrononauts.

From the official description:


  What would YOU do with a Time Machine? Would you stop the sinking of the Titanic? Prevent the assassination of JFK? Kill Hitler before WWII? These are just a few of the possibilities in Chrononauts, the award-winning card game of time travel. To win, you must change history at key points called Linchpins, so that history transforms into the Alternate Reality your character calls home. You can also win by collecting a specific set of Artifacts, such as a live dinosaur, the Mona Lisa, and an unpublished Shakespearean play. But be careful - if you create too many paradoxes, you could destroy the entire universe!