 Among strategies that do allow dependence on previous interaction, Batali and Kitcher like an analog of GRIM that they call Discriminating Altruist (henceforth DA). DA cooperates with any player that has never defected against it, and otherwise refuses to engage. They show that, among a group of five simple strategies, there will be a cyclic pattern like that described above in which “anti-social” (defecting) strategies are replaced by “asocial” (non-engaging) strategies, which are replaced in turn by “social” (DA) strategies, which are replaced again by “anti-social” strategies. Their analysis, however, leads them to conclude that if members of a population are restricted to these five strategies, evolution will lead them to spend “most of their time in states of high cooperation,” (though not as much as would be the case in a “fully optional” game where, in each round, only those who accurately signal a willingness to engage are paired). Simulations among agents who are permitted any strategies where a move depend on the two previous moves of its opponent are said to provide rough corroboration. Some caution is in order here. There is little analysis of which strategies underlie the cooperating populations in the simulations and, indeed, DA is not an option for an agent whose memory goes back only two games. Oddly, slightly less cooperativity is reported for the fully optional version of the game than for the semi-optional (though in each case, as would be expected, cooperativity is significantly greater tha n for the ordinary PD). The evolutionary dynamics employed and the measures of cooperativity employed are sufficiently idiosyncratic to make comparisons with other work difficult. Despite all these caveats, it seems safe to conclude that taking engagement to be optional can provide another explanation for the fact that universal, unrelenting defection is rarely seen in patterns of interaction sometimes modeled as evolutionary PDs.