Taken from www.FT.com
Dear Economist
Published: January 26 2007
Dear Economist,
My wife knows that my conference-going activities enable me to carry on a long-standing affair. Now she has the opportunity to exact her revenge: I am continuing the dalliance at a conference abroad, but my wife says she plans to bring some girlfriends to holiday in the same place. It would be a catastrophe if she were to make a scene by introducing them to my mistress, which is clearly her intention. I cannot hide. My mistress will demand to be taken out, and there are only one and a half decent restaurants in the town. Can you assist?
Yours sincerely,
“Mr Smith”, London
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Dear “Mr Smith”,
Textbook farce and textbook game theory – how delightful! Clearly, you cannot make a predictable dinner booking, otherwise your wife will certainly catch and humiliate you. At the same time, her own arrangements must also be unpredictable if she wishes to outsmart you.
If both restaurants are equally good, game theory suggests a simple strategy: you should choose at random, and so will your wife. As long as you are unpredictable, she will not wish to change her strategy, and vice-versa.
You hint that one restaurant is mediocre, but your strategy should not shift: toss a coin to choose where to go. Space does not permit me to share the relevant algebra, but be assured that your wife will be more likely to await you at the restaurant you prefer, which is why you might as well choose at random.
Most likely you will either be caught or endure a terrible meal. Your wife has arranged a game of strategy that you will probably lose. Perhaps it is time for the end of the affair?
Game theory: How it relates to the real world!