Two TDT players have 3 plausible outcomes to me, it seems. This comes from my admittedly inexperienced intuitions, and not much rigorous math. The 1st two plausible points that occurred to me are 1)both players choose C,Y, with certainty, or 2)they sit at exactly the equilibrium for p1, giving him an expected payout of 3, and p2 an expected payout of .5. Both of these improve on the global utility payout of 3 that's gotten if p1 just chooses A (giving 6 and 3.5, respectively), which is a positive thing, right?

The argument that supports these possibilities isn't unfamiliar to TDT. p2 does not expect to be given a choice, except in the cases where p1 is using TDT, therefore she has the choice of Y, with a payout of 0, or not having been given a chance to chose at all. Both of these possibilities have no payout, so p2 is neutral about what choice to make, therefore choosing Y makes some sense. Alternatively, Y has to choose between A for 3 or C for p(.5)*(6), which have the same payout. C, however, gives p2 .5 more utility than she'd otherwise get, so it makes some sense for p1 to pick C.

Alternatively, and what occurred to me last, both these agents have some way to equally share their "profit" over Classical Decision Theory. For however much more utility than 3 p1 gets, p2 gets the same amount. This payoff point (p1-3=p2) does exists, but I'm not sure where it is without doing more math. Is this a well formulated game theoretic concept? I don't know, but it makes some sense to my idea of "fairness", and the kind of point two well-formulated agents should converge on.