In acausal PD, (C, C) stands for bargaining, and bargaining in a different game could be something more complicated than carrying out (C, C). Even in PD itself, bargaining could select a different point on the Pareto frontier, a mixed outcome with some probability between (C, C) and (C, D), or between (C, C) and (D, C). So with acausal coordination, PD should play in three stages: (1) players establish willingness to bargain, which is represented by playing (C, C) in acausal PD (but not yet making moves in actual PD), (2) players run the bargaining algorithm, which let’s say selects the point 0.8*(C, C) + 0.2*(D, C), and (3) a shared random number samples let’s say (D, C), so the first player plays D and the second plays C.

In acausal PD, (C, C) stands for bargaining, and bargaining in a different game could be something more complicated than carrying out (C, C). Even in PD itself, bargaining could select a different point on the Pareto frontier, a mixed outcome with some probability between (C, C) and (C, D), or between (C, C) and (D, C). So with acausal coordination, PD should play in three stages: (1) players establish willingness to bargain, which is represented by playing (C, C) in acausal PD (but not yet making moves in actual PD), (2) players run the bargaining algorithm, which let’s say selects the point 0.8*(C, C) + 0.2*(D, C), and (3) a shared random number samples let’s say (D, C), so the first player plays D and the second plays C.