in an approximately cubic function
I am curious; how did you figure that out?
Well, it was a given that it wasn't a linear equation, because ten minutes playing Devil Survivor can't yield one-fourth of a battle finished. I was fairly confident that it was a polynomial expression, however, since in matters like writing and reading eventually there's only so much you can take. Roleplaying is an activity that's definitely better than quadratic - if I spend two hours straight on it at the right time, my companions and may well get six dozen responses in, while distributing that activity randomly over three days is more likely to yield about a dozen responses. So I picked cubic. I haven't actually done any regression on it yet (it was midnight my time when I submitted this).
This has been bothering me ever since I started trying to use rationalist techniques to make better decisions (like anti-akrasia ones). The only field related to rationality I knew much about was game theory, but to my disappointment basic game theory has only increased my problems due to a certain formulation I can't abandon.
The Volunteer's Dilemma (http://en.wikipedia.org/wiki/Volunteer's_dilemma) is in essence the Prisoner's Dilemma with more players - which means that defection is an even more dominant strategy. The problem is that the decision whether to do unpleasant tasks becomes a Volunteer's Dilemma with multiple future selves as my competition - 4:00 tenshiko, 4:15 tenshiko, 4:30 tenshiko, and so on. Although the incentive to defect should decrease as time goes on, there's the problem of how 9:00 tenshiko can easily defect in an even more effective fashion and bring in 11:00 tenshiko and 11:15 tenshiko to further level the playing field. There is the further problem that, given how many of my current hobbies convert time to reward in an approximately cubic function, the incentive is high for 6:00 tenshiko, 7:00 tenshiko, and 8:00 tenshiko to form coalitions.
I guess what I'm really asking for is a more advanced matrix that represents the diminishing returns of bringing in other future selves, such as went-to-bed-at-1:00 tenshiko and completely-bombed-that-test-at-10:00 tenshiko, or at least the diminishing probability over time that "it doesn't matter, 9:45 tenshiko can take care of it".
If this goes well, I will probably try to flesh out the material received in responses with what I already know and produce a post in main discussing time management and its relation to game theory.