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Friday, 6 May 2011


When you walk down a corridor and someone is behind you, it is obviously polite to hold any doors you encounter open for them.  They arrive at the door, put their hand on it to hold it open, and you walk on while they walk through.  If they too are polite they will say, "Thanks."

But if it is a long corridor with many doors, you will find yourself holding each and all of them for your follower.  After about three doors this becomes a slight embarrassment to you both.  Your follower will grin at you sheepishly and make I-am-hurrying-up gestures  as they approach.  You will smile back with a slight air of condescension.

It would make a bit more sense to swap: you hold Door 1 for them while they walk through, they (now ahead) hold Door 2 for you while you walk through that, and so on.  For some reason we never do this.  Maybe it is because the follower feels that - if they were to walk ahead - they would be usurping your leader's position, and that that would be presumptuous.   This is despite the fact that the swapping scheme would allow them to return your favour at the next door - immediate reciprocal altruism.

The swapping scheme even extends to arbitrarily many people walking down an infinite corridor with doors: the leader holds the next door for everyone, then joins the back of the procession.  (Though why a bunch of people would want to walk in Indian file down an infinite corridor I'm not quite sure.)

Game theoretically, of course, the Nash equilibrium is the selfish let-the-door-go-in-the-follower's-face strategy; the equivalent of defaulting in Prisoner's Dilemma.  But - as we all know - people don't behave like the individual self-interested rational actors of naive game theory because our utility function is not individual advantage, it is the advantage of the genes that we both carry and share with others.

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