As you may have read in the parameters section, Robert Axelrod constructed a tournament that had strategies, similar to the ones you defined here, competing against each other. Some of these strategies were quite complex, but in general the one that performed the best had the simple rule "play the strategy that your opponent played last time," and also included the provision for starting out cooperating. This rule has come to be known as Tit-For-Tat (TFT), and has received a lot of attention in the literature. In particular, this strategy has come to be associated with reciprocal altruism in which an individual repays an act of cooperation with a like act of cooperation.
The strategy of Tit-For-Tat has been demonstrated in sticklebacks (Milinski, 1987. TIT FOR TAT is sticklebacks and and the evolution of cooperation. Nature 325: 433- 435.), bats (Wilkinson, 1984. Reciprocal food sharing in the vampire bat. Nature 308: 181-184.) and tree swallows (Lombardo, 1985. Mutual restraint in tree swallows: A test for the TIT FOR TAT model of reciprocity. Science 227: 1363-1365).
Tit-For-Tat does not perform the best in every situation, and others have proposed strategies that perform better in these situations. One of these strategies is known as "Pavlov," or win-stay, lose-shift. This strategy states that you should cooperate only if you played the same strategy as your opponent did last time. The name is derived from the fact idea that the "reflex like response" of an individual sticking with a strategy if rewarded by mutual cooperation, or by the "'sucker's payoff" (exploiting a cooperator), and changing strategies if punished by mutual defection or being exploited by a defector (Nowak and Sigmund, 1993. A strategy of win-stay, lost-shift that outperforms tit-for-tat in the Prisoner's Dilemma game. Nature 364:56-58.). The advantages of Pavlov over TFT are that it is more tolerant, and it cannot be invaded by pure cooperators.
Other strategies exist that perform well, some of which are beyond the realm allowed in this particular implementation. For example, generous tit-for-tat cooperates after an opponent's cooperation, but unlikely TFT will also cooperate after an opponent's defection with some probability.
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