Siblings Sacha and Simon love basketball—and there’s nothing better for a basketball fan than March Madness! If they had the chance to attend an NCAA tournament game today, each would value an Elite Eight game at $1,000, a Final Four game at $1,600, and a Championship game at $1,800. A benevolent aunt offers Sacha and Simon one ticket each to a game of their choosing: Elite Eight, Final Four, or Championship. But there’s the hitch; the benevolent aunt is slightly controlling! The siblings can attend an Elite Eight game this year, but if they choose a Final Four game, they’ll have to wait one year, and if they want to see the Championship game, they’ll have to wait for two years.

a. Suppose Sacha discounts each year of waiting at 10%. Which option will she choose today?

b. Suppose Simon discounts hyperbolically so that something a year away is always discounted at 30%, while horizons beyond the first year are discounted at 10%. Which option will Simon choose today? 

c. Next year, Simon and Sacha’s aunt tells them, “You’ve waited so patiently. If you’d like to see the Final Four game today, you can. Or, you can wait and see next year’s Championship game.” What will Simon and Sacha do?

d. Explain why Sacha’s preferences are time-consistent, but Simon’s aren’t.