January 2, 2013

Rethinking Tit-for-Tat

By Art Hinshaw

Many of us use a version of the prisoner’s dilemma game as part of our negotiation courses.  In the game, participants have the choice of cooperating with others to get a minimal reward, or they can increase their winnings by taking advantage of everyone else.  After the students play the game, I introduce Robert Axelrod’s game theory tournaments from the late 1970s in which tit-for-tat was the most successful strategy.  Essentially the strategy is to follow that of your counterpart:

  • Cooperate until provoked,
  • If provoked, retaliate,
  • Forgive quickly – in other words, cooperate after the counterpart cooperates,
  • Repeat as conditions require.

The tit-for-tat strategy has had a wide range of applications from biology to political science to negotiation, among many others.    But now the Chronicle of Higher Education reports that physicists William H. Press (Texas) and Freeman J. Dyson (Princeton) have come up with a strategy, known as the zero determinate strategy, that outperforms tit-for-tat.   The Chronicle describes the strategy as follows:

If the opponent cooperated in the previous turn, the computer runs a formula to decide what to do next. If the opponent didn’t cooperate, it runs a different formula. The program doesn’t pay attention to the history of choices nor does it have any theory of the opponent’s mind. It’s a formula based only on the previous decision. But playing against a dumb opponent—one who is just trying to do the best he or she can—the formulas regularly rise to the top.

Therein lies the strategy’s weakness, one’s counterpart(s) being unaware.   According to the MIT Technology Review:

The one caveat is that the other player must be unaware that they are being manipulated. If they discover the ruse, they can play a strategy that results in the maximum jail time for both players: ie both suffer. . . . . The interesting thing here is that when both players are aware of the zero determinant ruse, the prisoner’s dilemma turns into a different game [the Ultimatum Game].

Also intriguing is that the MIT article calls tit-for-tat “a special case of the zero determinate strategy.” 

At this point I’m not sure how I’m going to incorporate this into my class.  But I surely won’t use the Chronicle’s title for it’s article about the new strategy – To the Trickster Go the Spoils.

Last 5 posts by Art Hinshaw

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