optimal group rationality doesn’t necessarily mean that each individual in the group has optimal individual rationality.
Nitpick: Only if “the group” and “the individual” don’t have the exact same utility function and/or that either optimal rationality is not common knowledge within the group or not all individuals are optimal—which all seems rather suboptimal for “optimal group rationality”, but not excluded.
If all group members have knowledge that all group members are optimal, and all of them care about the group utility function rather than individualistic interests, they will all randomize who has the sub-personally-optimal strategy. Just like in the Rationalist vs Barbarians scenario.
Nitpick: Only if “the group” and “the individual” don’t have the exact same utility function and/or that either optimal rationality is not common knowledge within the group or not all individuals are optimal—which all seems rather suboptimal for “optimal group rationality”, but not excluded.
If all group members have knowledge that all group members are optimal, and all of them care about the group utility function rather than individualistic interests, they will all randomize who has the sub-personally-optimal strategy. Just like in the Rationalist vs Barbarians scenario.