Pretty simple because time isn't discrete in this puzzle. Assuming they are logical as well, both of you know you can't keep walking forward in the dark withou

Pretty simple because time isn't discrete in this puzzle. Assuming they are logical as well, both of you know you can't keep walking forward in the dark without risking bumping. If you change sides, they could as well. So you both stop waking and the lights turn on. Because you both know time isn't discrete, if the lights go out and you weren't moving, then it was your partner that was moving. The person who initiates the darkness gets to move. Wait a random amount of time and if the lights didn't go out, swap sides of the hallway. Once the swap is done (by the one who moved first) and you both see you are no longer going to collide, both resume waking forward.