The Give and Take of Tit For Tat

Network analysis sheds light on the structure of an organization but tends to reduce individual relationships to "yes" or "no" decisions. What happens when the answer is "it depends"? The analytical among us must turn to other branches of mathematics for some measure of reason.

Game theory in particular has a lot to say about the give and take of everyday relationships. This branch of mathematics may owe most of its fame to Russell Crowe's performance as John Nash in "A Beautiful Mind." Since John Nash's heyday of the 1950s, game theory has also been put to good use by evolutionary biologists, who have shown how touching acts of seeming altruism (such as caring for a sick sibling) in fact occur precisely to the degree that they produce maximal genetic survival of the allegedly altruistic organism. See Richard Dawkins for utterly fascinating reading about this.

Lately I have been thinking about another question of game theory: what is the optimal way to build a trusting and mutually profitable relationship with a colleague? Give away too much too soon and you will be taken advantage of. Never give at all and you will probably receive nothing in return. Here's a classic result showing how a surprisingly simple strategy produces almost unbeatable results over the long haul. The strategy is called "Tit For Tat" and boils down to this: Assume the best and start by giving a little. Then the next time you see the same colleague again, simply return the same dose of "give" or "take" that he extended your way in your last encounter.

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Doing research for this article, I discovered that the "Tit For Tat" strategy referenced above has finally been defeated after a 20-year reign. The new strategy requires a team of competitors to collude: most of the teammates sacrifice their own well-being so that a handful of team leaders win it all. Sounds just like the winning strategy at the Tour de France.