Excellent post, excellent sequence. Advanced game theory is definitely something rationalists should have in their toolbox, since so much real-world decision-making involves other peoples' decisions.

Here there are a nearly infinite number of possible choices ... these are all Nash equilibria. Despite this mind-boggling array of possibilities, in fact all six episodes of this particular game ended with the two contestants meeting successfully after only a few days.

An interesting analysis when you have "nearly infinite" Nash equilibria, is the metagame of selecting which equilibrium to play. Do you plan on exploring this in the sequence?

Of course, specialness, like beauty, is in the eye of the beholder.

I strongly urge readers to explore this! What should you do if you suspect the other player beholds 'specialness' in a different way to you? Does your plan of action change if you suspect the other player also suspects a difference in beholding?