Frozen Evolution. Or, that’s not the way it is, Mr. Darwin. A Farewell to Selfish Gene.

From the viewpoint of game theory, even the Generous Tit for Tat strategy is not an evolutionarily stable strategy in the stochastic world, because its temporary success enables the always cooperate strategy to spread and this allows the successful return of the always betray strategy. So the game does not have a stable solution, and the representation of individual strategies in the population circulates constantly. It seems so far that the only evolutionarily stable strategies are those that do not direct their behavior according to the opponent’s behavior in the last round, but according to how they behaved in the last round and what profit they got from it. A fairly successful, even though not evolutionarily stable strategy of this kind is a strategy named Pavlov (Nowak & Sigmund 1993). It is directed by a simple rule: repeat your behavior from the last round, if it was successful (i.e. you betrayed and the opponent cooperated or you both cooperated), change your behavior if you lost in the last round (i.e. you cooperated and your opponent betrayed or you both betrayed).  The Pavlov strategy, similar to the Generous Tit for Tat, does not allow the always cooperate strategy to spread in the somewhat unpredictable world, but it enables the always betray strategy to spread. Existing results show that even the simplest so-far described evolutionarily stable theories have to be capable of learning, i.e. they must have memory and the ability to remember the results of a number of previous rounds when choosing a strategy for a new round (Wakano & Yamamura 2001). Experiments performed using experimental games with human volunteers have shown that, actually, in a normal population, people mainly follow strategies similar to the Generous Tit for Tat as well as the Pavlov strategy (Fig. XVI.6). At the same time, it has been shown that the actually used strategies were somewhat complicated and also more successful than the Generous Tit for Tat or Pavlov and that the players used information from a number of previous rounds in the strategies (Wedekind & Milinski 1996).