Aha - at http://www.pnas.org/content/109/26/10409.full.pdf , zero-determinant strategies are defined by two factors, chi and phi, and at least when chi is 1, maximum phi results in the strategy of Tit-for-Tat, which is exactly what I was looking for.
Hm... is there a mathematical notation for the maximum of a variable, like |x| indicates the absolute value of x?
In addition, when chi is at the extortionate level of 3.5, then when phi is maxxed out, the odds of player X cooperating if player Y cooperated last turn are 66.6% or 50%, depending on whether player X also cooperated on the previous turn. Thus, in order to give player Y enough of an incentive to want to cooperate - providing odds of at least 50% of ending up with CC - player X may have their own incentive to set chi to something below 3.5. As it happens, there are two mathematical constants a little below that that might be chosen - the inverse Fibonacci constant, also called psi, about 3.36, or the more widely-known pi, 3.14.
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