Everyone knows the old Alphonse and Gaston routine, right? Two guys trying to go through a door, but the keep deferring to one another rather than one of them just going through already?
Well, I see that happen at my shuls all the time, and there often is some creative jockeying for position. One morning I was walking into shul. Someone was holding the door already, and Avi and I were about to pass through. I gestured to Avi to go first, and he handed me his siddur. As soon as I took it, he said "You're holding a sefer, you go first." Point to Avi.
This past Shabbat at Shalosh Seudah I was trying to go through a door after washing before eating bread, and Yaakov was trying to pass through the door the other way. He smiled, backed out of my way and said "You're doing a mitzvah, you take priority." Point Yaakov. On the way out after benching, we got tangled up in the door again and I told him "You're the zaken (elder, wiser one), you go first." He looked a little hurt and said something about "I'm not sure that was fair" but he went through anyway. Point me.