Yawning is more about getting more oxygen in your system. Which sometimes can be due to you being sleepy and not breathing as well as normal, but not always to do with tiredness.

I think when you see someone else yawn, you do the same to make sure you're just as on point as they are. Since more oxygen in your system means you'll operate more efficiently.

I think that's correct, anyway? If someone knows better, please correct me