Any time travel story about going back to meddle with time are inherently paradoxical. I need help resolving this.
Here's an example of the problem for discussion:
1. Roberta is born.
2. Roberta becomes a lethal assassin.
3. Roberta assassinates Samir.
4. Time travel is invented.
5. Chang wishes Samir were still alive.
6. Chang goes back in time to stop Samir's assassination.
...2.5' Chang kills Roberta.
...3' Roberta does not assassinate Samir.
...3.5' Chang returns to his normal timeline.
7. Hey, Samir is still alive!
Ignoring that Chang miraculously remembers both timelines, and ignoring possibilities about a self-correcting universe that prevents Chang from killing Roberta or kills Samir by other means, you still have this problem:
5' Samir is still alive.
6' Chang has no reason to go back in time to stop Samir's assassination.
That is, going back in time to change it necessarily destroys your motivation for going back in time to change it, and is thus paradoxical.
How can I get around this for a game about time travel?