 Nowak and Sigmund simulated two kinds of tournaments that avoid the three questionable features. The first examined the family of “reactive” strategies. For any probabilities \(y\), \(p\), and \(q\), \(\bR(y,p,q)\) is the strategy of cooperating with probability \(y\) in the first round and thereafter with probability \(p\) if the other player has cooperated in the previous round, and with probability \(q\) if she has defected. This is a broad family, including many of the strategies already considered. \(\bCu\), \(\bDu\), TFT, and Cp are \(\bR(1,1,1)\), \(\bR(0,0,0)\), \(\bR(1,1,0)\), and \(\bR(p,p,p)\). GTFT, when payoffs are \(5,3,1,0\), is \(\bR(1,1,.25)\). To capture the inevitability of error, Nowak and Sigmund exclude the deterministic strategies, where \(p\) and \(q\) are exactly \(1\) or \(0\), from their tournaments. As before, if the game is sufficiently long (and \(p\) and \(q\) are not integers), the first move can be ignored and a reactive strategy can be identified with its \(p\) and \(q\) values. Particular attention is paid to the strategies close to Molander's GTFT described above, where \(p=1\) and \(q = \min \{1-(T-R)/(R-S), (R-P)/(T-P)\}\). The first series of Nowak and Sigmund's EPD tournaments begin with representative samples of reactive strategies. For most such tournaments, they found that evolution led irreversibly to \(\bDu\). Those strategies \(\bR(p,q)\) closest to \(\bR(0,0)\) thrived while the others perished. When one of the initial strategies is very close to TFT, however, the outcome changes.