Let's assume running is linked to the utility on the day you run and on the following day. Assume that running gives you U = -6 on the day you run and U = 8 on the day after.

Your discounted utility is provided by the formula:

Discount(t) = ^t

1) If you have = 1, = 0.5, would you run today?

2) Do you want to run tomorrow?

3) Let's assume Sophistication: You are fully aware of your future self-control problems

Naivete: You are fully unaware of your future self-control problems.

If you are nave, will you run or not run tomorrow?

4) What what value should have for you to run today?

5) Assume = 0.5, and that if you run following day you getU = 8. What would U need to be on the day you run to run today?

6) Imagine you are partially nave. Your true = 0.5 but you think = 0.6 in the future). Do you think you will run tomorrow?

Source: Practice Problems