Axelrod attributed the success of
TFT to four properties. It is
nice, meaning that it is never the first to defect. The eight nice entries in Axelrod's tournament were the eight highest ranking strategies. It is
retaliatory, making it difficult for it to be exploited by the rules that were not nice. It is
forgiving, in the sense of being willing to cooperate even with those who have defected against it (provided their defection wasn't in the immediately preceding round). An unforgiving rule is incapable of ever getting the reward payoff after its opponent has defected once. And it is
clear, presumably making it easier for other strategies to predict its behavior so as to facilitate mutually beneficial interaction.
Suggestive as Axelrod's discussion is, it is worth noting that the ideas are not formulated precisely enough to permit a rigorous demonstration of the supremacy of
TFT[...]Evidence has emerged that the striking success of
TFT in Axelrod's tournaments may be partly due to features particular to Axelrod's setup. Rapoport et al (2015) suggest that, instead of conducting a round-robin tournament in which every strategy plays every strategy, one might divide the initial population of strategies randomly into equal-size groups, conduct round-robin tournaments within each group, and then a championship round-robin tournament among the group winners. They find that, with the same initial population of strategies present in Axelrod's first tournament, the strategies ranked two and six in that tournament both perform considerably better than top-ranked
TFT. Kretz (2011) finds that, in round-robin tournaments among populations of strategies that can only condition on a small number of prior moves (of which
TFT is clearly one) relative performance of strategies is sensitive to the payoff values in the PD matrix. (Interestingly, this is so even if the PDs all satisfy or fail to satisfy the condition R+P=T+S, characterizing exchange games, and if they all satisfy or fail to satisfy the RCA condition, R>½(T+S).
Equally telling, perhaps, are the results of a more recent tournament using the same parameters as Axelrod did. To mark the twentieth anniversary of the publication of Axelrod's book, a number of similar tournaments were staged at the IEEE Congress on Evolutionary Computing in Portland in 2004 and the IEEE Symposium on Computational Intelligence and Games in Colchester 2005. Kendall et al 2007 describes the tournaments and contains several papers by authors who submitted winning entries. Most of the tournaments were deliberately designed to differ significantly from Axelrod's (and some of these are briefly discussed in the section on signaling below). In the one that most closely replicated Axelrod's tournaments, however,
TFT finished only fourteenth out of the fifty strategies submitted.
[...]
Li (2007) says explicitly that the idea behind
APavlov was to make an educated guess about what strategies would be entered, find an accurate, low-cost way to identify each during the initial stages of the game and then play an optimal strategy against each strategy so identified. For example, the strategies
Cu,
Du,
GRIM,
RANDOM,
TFT,
TFTT,
TTFT, and
P1, described in a
supplementary table, had all appeared in previous tournaments. By defecting in round one, cooperating in round three, and choosing the opposite of one's opponent's round-one move in round two, one could identify any opposing strategy from among these nine in three moves. This identification process would be costly, however, because, by its first move, it eliminates any opportunity of cooperation with
GRIM. Li chooses instead to employ
TFT over the first six rounds as his identifying strategy, reducing cost at the expense of accuracy and range. It is worth noting that
TFT cannot distinguish any pair of strategies that satisfy Axelrod's niceness condition (never being the first to defect). This means that it forgoes the chance to exploit unconditional cooperators. Li's entry won its tournament only because he guessed correctly that not many unconditional cooperators would be present.
