The game uses a "sprint" mechanic instead. To run, you need to hold down the R1 button (right trigger) while moving.
It's worth noting that running in Fallout: New Vegas comes with a few drawbacks:
* Stamina depletion: Running consumes your character's stamina, which will eventually require you to stop and rest.
* Noise: Running makes significantly more noise than walking, attracting enemies more easily.
So, while there's no "run" button, the "sprint" system allows for a more tactical and strategic approach to movement in the game.