Clearly JW was trying to maximize the joint payoff, which makes sense only if you he is being paid in dollars and is going to split them with AA after the game.

AA on the other hand was trying to maximize his own payoff and achieve a more equitable outcome by getting JW to sacrifice 2 points in order to give him one.

Since JW seemed to think he was playing plain-vanilla PD he totally failed to form any kind of theory as to why AA was acting as he did, and the result was disappointing for both of them.

(Of course he may not have been inclined to cooperate if he had, though research shows that even chimps are willing to pay a high personal price to punish unfairness in others, so he should have been aware at the very least).

On the other hand, since they had to spend a lot of points on learning the game, and operating what was essentially a very expensive telegraph, the outcome was not that bad.

So no, I don’t think JW was “the smart one”. As for thinking it is smart to understand “that it was the two of them playing the umpire” — that’s not smart, that’s dumb. The umpire is not an active participant in the game. AA was correct, he was playing against JW.