New "zero determinant" strategy discovered for Prisoner's Dilemma

[phantom power]

Until now, everyone thought the best strategy in iterative prisoner's dilemma was to copy your opponents behaviour in the previous round. This tit-for-tat approach guarantees that you both spend the same time in jail.

That conclusion was based on decades of computer simulations and a certain blind faith in the symmetry of the solution.

So the news that there are other strategies that allow one player to not only beat the other but to determine their time in jail is nothing short of revolutionary.

The new approach is called the zero determinant strategy (because it involves the process of setting a mathematical object called a determinant to zero).

It turns out that the tit-for-tat approach is a special case of the zero determinant strategy: the player using this strategy determines that the other player's time in jail is equal to theirs. But there are a whole set of other strategies that make the other player spend far more time in jail (or far less if you're feeling generous).

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.

http://www.technologyreview.com/view/428920/the-emerging-revolution-in-game-theory/?ref=rss

[Jim Lane]

1. The focus on "winning" in this sense isn't all that important.

The linked article seems to assume that doing well in the game means spending less time in jail than the other player. The more sensible interpretation, however, is that doing well means minimizing your own jail time.

Consider two outcomes, averaged over the course of multiple iterations: (1) Alice spends 2 months in jail and Bob spends 4 months in jail. (2) Alice and Bob each spend one month in jail.

It's short-sighted to say that #1 represents a "win" for Alice. She does better in #2 than in #1. Moving from #2 to #1 hurts both players but it's pointless to commend the change to Alice just because it hurts her less than it hurts Bob.

[phantom power]

2. that is true, and also....

even more than minimizing my jail time, this class of new strategies seems to be about controlling my opponent's outcome. So, forgetting for a moment my outcome, this can be about manipulating my opponent in some way (win, lose, sideways).

In that regard, it may have real implications for business, or political science, or war. Getting your opponent To Do Things, even on a temporary basis, is a tool in the toolbox.