Tangential, but I hit this issue very often with couple of friends during university years; two of us wanted to go through a door, and get stuck in a "you go", "no, you go", "I insist" loop. At some point I said, "you know what, let's do rock-paper-scissors, if you lose you go first". It immediately caught on with my friends, and ever since that, when attempting to go through a door at the same time, we'd just exchange looks, and immediately play a wordless round of rock-paper-scissor to resolve the conflict, while the rest of the class looked at us and asked "WTF just happened?!".