I totally agree and would add one more detail...

Attitude!
If the guys are chickens (mostly the same without a "Clooney") the moment of choice for the "one" would change the attitude of them all upon arrival to the girls and distract them also focusing on the outcome of the "one" with the "blonde", avoiding their total attention to their "brunette" piece of the cake.

The Nash solution considers no negative change of attitude, by the contrary I would agree it adds a bit of positive attitude to the guys knowing they are all balanced and agreed upon one same "common wealth" with the same effort needed for everyone, dealing with no predisposed psychological threats or less chances by anyone but the "blonde" (the least effort and sacrifice for both groups for the best outcome of all involved individuals).