Repeat Worked-Out Problem 13.1 with the following twist: assume that, despite his self-control problem, Matt naively (and mistakenly) believes that he will follow through with the plans he makes on any given day. When will he do the chore? Will it be earlier or later than if he correctly anticipates his inability to follow through on certain plans? Why?
In Problem 13.1
It's Tuesday and Ted is making plans for the end of the week. There are parties on Wednesday, Thursday, Friday, and Saturday nights. He has a big test on the following Monday, so he only has enough free time to go to one party. The parties get better later in the week. He expects Wednesday's party to be pretty lame (payoff of 4), Thursday's party to be better (payoff of 7), Friday's party to be excellent (payoff of 12), and Saturday's party to be awesome (payoff of 20). If he attends no party on a given day, his payoff for that day is zero. Ted behaves as follows. On any given day, he wants to maximize the utility function 2PN + PF, where PN is the payoff on that day and PF is the sum of his payoffs on future days. To illustrate, suppose he goes to the party on Friday. Then his utility from Thursday's perspective will be 12, but his utility from Friday's perspective will be 24. When deciding whether to go to the party on any given day, Ted correctly anticipates how he will behave on subsequent days. As of Tuesday, which party would Ted like to attend? Which party will he actually attend? Why?