Time After Time
Two time travelers, Alexa and Bertram, pursue each other through the decades in a deadly cat-and-mouse chase. She is the last survivor of a 1960s research project studying time travel; he is a soldier desperate to wipe out any trace of Alexa's research, including perhaps Alexa herself. Each of them is armed with a time machine, but these machines have a very special rule: They can only move forward in time, never backward. To save herself, Alexa must leap further and further into the future, with Bertram never far behind.
Caught in the crossfire between Alexa and Bertram is Spatz, a teenager from the 1990s who tries to help Alexa but instead gets dragged along with her into another time. In this nightmarish future, everyone has their own personal time machine and people pass the time watching gruesome spectacles such as the Time Games, a gladiator-style death match that kidnaps unwitting combatants from throughout history and forces them to fight each other for sport. Now, they must survive the Time Games and escape from this surreal dystopia.