It's kinda tempting to write here: "It is a metaphor for " and just leave it like that. I wonder how many people would find an explanation for what that meant.
(Actually, it's a metaphor for dating. Just joking. It's obviously a metaphor for Unfriendly Oracle AI playing Prisonner's Dilemma against a Causal Decision Theory. Unless that also is somehow a metaphor for dating.)
Let's suppose you start with $1000 to invest, and the only thing you can invest it in is stock ABC. You are only permitted to occupy two states:
* All assets in cash
* All assets in stock ABC
You incur a $2 transaction fee every time you buy or sell.
Kind of annoying limitations to operate under. But you have a powerful advantage as well. You have a perfect crystal ball that each day gives you the [probability density function](http://en.wikipedia.org/wiki/Probability_density_function) of ABC's closing price for the following day (but no further ahead in time).
What would be an optimal decision rule for when to buy and sell?