Dear Economist,

My work recently took me to New York, where it kept me until Saturday morning. I invited my girlfriend to visit so we could spend the evening there together. As we split most big costs in our relationship, I proposed we share the cost of the hotel room and she cover her air fare. She argued that because my company had covered my air fare, I should split hers with her. I countered that either the utility of spending a nice evening in the city (during which I would have undoubtedly picked up dinner and the rest of the evening), was worth it to her, or it wasn’t. Who is right?

Kind regards,

John Wegman, by e-mail

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Dear John,

You have thought about this problem in entirely the wrong way. Both you and your girlfriend have a case, but this disagreement is part of a much wider game.

Your trip has created joint gains for the pair of you and you are arguing over how to divide the spoils. There is no right way to do this. Your admission that you would pay for dinner and entertainment, although you normally split major costs, is an admission that the merits of the case are vague.

You might think that some fancy economic theorem will give you a precise answer. Nothing could be further from the truth. You will have such arguments many times, and game theory shows that in an indefinitely repeated game, there are many possible outcomes, some good and some bad. The best are co-operative and profitable for both players - which suggests a little generosity on your part may go a long way.

Of course, you have everything to gain from penny-pinching if your relationship with your girlfriend is short-lived. You are going the right way about it.

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