12th June, 2004

Dear Economist,

My close circle of friends follow a scheme of “tour accounting”, the basis of which is that we never really bother who pays the bill, because, as we plan to remain friends for a lifetime, it will work out in the long run.

Is this sensible economically?

— Ruth Kirby, Surrey

Dear Ms Kirby,

Your inventive scheme mixes high risks with high rewards. The rewards are twofold: first, a massive saving on transaction costs. The late humorist Douglas Adams, who surely could have been an economist, theorised that the calculations involved in splitting a restaurant bill were so nonsensical as to deserve their own branch of surreal mathematics, called “Bistromathics”. Your system means that the waiter need not swipe a dozen credit cards for each meal and that you and your friends need never bother themselves with Bistromathics.

Second, each time a person picks up the bill, she is sending a signal that she expects to be in the friendship long enough to be paid back. Life with your friends is an endless sequence of credible signals of friendship – a real love-in for the economically literate. Sadly, you are making a mistake common to many junior game theorists: the equilibrium you describe is unstable in the face of entry. Pseudo-friends have an incentive to join your group, freeload on its generosity until challenged, and then walk away in debt to the tune of several meals.

Your only rational response is to require any new friends to pay a substantial deposit when they join your circle. Their early obligations could be paid out of the deposit, which would be forfeited in the event of non co-operative behaviour. Such a scheme will ensure that excess entry is not a problem that will trouble your circle of friends.

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