 After publication of Axelrod, 1984, a number of strategies commonly thought to improve on TFT were identified. (Since success in an IPD tournament depends on the other stragies present, it is not clear exactly what this claim means or how it might be demonstrated.) The first of these was Nowak and Sigmond's Pavlov, also known as, Win-Stay Lose-Shift (WSLS), which conditions each non-initial move on its own previous move as well as its opponent's. More specifically, it cooperates if it and its opponent previously moved alike and it defects if they previously moved differently. Equivalently, it repeats its move after success (temptation or reward) and changes it after failure (punishment or sucker). Hence the names. This strategy does well in environments like that of Axelrod's tournment, but poorly when many unconditional defectors or random players are present. It is discussed further under the label \(\bP_1\) in the sections on error and evolution below. A second family of these is Gradual Tit for Tat (henceforth GrdTFT). GrdTFT differs from TFT in two respects. First, it gradually increases the string of punishing defection responses to each defection by its opponent. Second, it apologizes for each string of defections by cooperating in the subsequent two rounds. The first property ensures that (unlike TFT) it will defect with increasing frequency against a random player. The second ensures that (unlike TFT) it will quickly establish a regime of mutual cooperation with suspicious versions of TFT (i.e., versions of TFT that defect on their first move). Beaufils et al show that the version of GrdTFT in which the string of defections is increased by one each time it is exploited wins round robin tournaments populated by a selection of “good” IPD strategies (including TFT) that the authors chose after an examination of previous tournaments. Tzafestas (1998) argues that, in making a each move depend on the entire prior history of the game, GrdTFT incorporates undesirable memory requirements. She suggests that equal success might be obtained with an "adaptive" strategy, that tracks a measure of the opponent's cooperativeness or responsiveness across a narrow window of recent moves and chooses its move according to whether this measure (the "world") exceeds some threshold. The critique seems misguided: maintaining a count of prior defections seems no more burdensome than updating the world variable. Nevertheless Tzafestas is able to show that one of the strategies she identifies outperforms both TFT and GrdTFT in the very same environment that Beaufils had constructed.