You don't even have to go that far from the original question. If instead of the entire world being a single game, if you have hundreds of millions of sub-games where 9 random people are placed within, what should you do?

Surely some of those groups are going to be filled with selfish red pickers. Should the kind coordinating players still go blue? All the red pickers are going to lie that blue is sensible. I suspect that more coordinators will die in this way than the always blue pickers if every coordinating player went red.

So now the full-world version only has the law of large numbers on their side, but they have no way of knowing just what percentage of the population is a selfish red picker. Going for team blue is the much riskier option that can yield catastrophe.