> 6. People who realize the game theory optimal strategy is to announce you're pressing blue and convince everyone else to press blue, but privately press red.

A lot of this analysis depends on accurately guessing how people will react, so it's probably hard to say any strategy is game theory optimal without a lot of unrealistic simplifying assumptions.

In a world where you're able to convince a lot of people anything, it might better to convince everyone to press red. If it looks like 99.99% of people will press red without your influence, you're probably best off spending your time convincing the .01% who might press blue not to do so.

It also has the upside of not making you a dirty liar. I wonder, what would Kant think about this hypothetical?