True, they will fail to cooperate for some R, but the values of such R have a low probability. (But yeah, it's also required that uy and R are chosen independently—otherwise an adversary could just choose either so that it results in the players choosing different actions.)

The smoothness comes in from marginalising a random R. The coordination comes from making R and ε common knowledge, so they cooperate using the correlation in their observations—an interesting phenomenon.

True, they will fail to cooperate for some R, but the values of such R have a low probability. (But yeah, it's also required that uy and R are chosen independently—otherwise an adversary could just choose either so that it results in the players choosing different actions.)

The smoothness comes in from marginalising a random R. The coordination comes from making R and ε common knowledge, so they cooperate using the correlation in their observations—an interesting phenomenon.

(How can I write LaTeX in the comments?)