The Emerging Revolution in Game Theory

100 and asking her to divide it between her and Bob. Bob can accept the division or refuse it if he thinks the division is unfair, in which case both players get nothing. The refusal is Bob's way of punishing Alice for her greed. 

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.

Press and Dyson's discovery has sent game theorists scurrying to work out the implications. They've been using prisoner's dilemma to gain insight into everything from Cold War politics and climate change negotiations to psychology and, of course, the evolutionary origin of co-operation itself. 

Today, we see one of the first paper's to study these implications in detail. Christoph Adami and Arend Hintze from Michigan State University in East Lansing investigate whether the zero determinant strategies are evolutionary stable. 

That's an interesting question. It asks the following: if an entire population of individuals all play zero determinant strategies, could another strategy spread through the population and take over? If not, zero determinant strategies are evolutionary stable.

Adami and Hintze show that zero determinant strategies are not evolutionary stable. The reason is that they do not perform well against each other and that leaves the door open for other strategies to sneak in and take over. 

Zero determinant strategies are not stable in another way. Adami and Hintze show that if the player's strategies evolve, the changes that occur between one generation and the next ensure that the new strategy is generally not zero determinant. So the strategy cannot survive. 

However, there is one scenario in which Adami and Hintze say the new strategy should be stable. That's when the zero determinant players can work out whether other players are using the same strategy or not. In that case, they can avoid the loses that occur when playing against their own while exploiting ignorant players. 

So to be stable, zero determinant strategies require additional information about their opponents.This information gives them a clear advantage but probably only a temporary one. "Such an advantage is bound to be short-lived as opposing strategies evolve to counteract the recognition," they say. 

In other words, the other players ought to develop a kind of camouflage that prevents them being spotted and exploited.

That may explain why nobody's found examples of zero determinant strategies in nature: in most cases they won't be stable and even if they are, the situation is likely to be short lived. As Adami and Hintze put it in the title of their paper: winning isn't everything.

That's not to say there aren't examples out there ready to be found. On the contrary. "This type of evolutionary arms race has been, and will be, observed throughout the biosphere,"  say Adami and Hintze. 

Of course, this is just the beginning of an entirely new approach to game theory that has profound implications. Suggestions for where it might have the most impact in the comments section please.

Ref: arxiv.org/abs/1208.2666: Winning isn't everything: Evolutionary stability of Zero Determinant strategies

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