Lecture 1 – here .
The general problem question for this week is the following, which I call the “Monte (Hall) Carlo game show”.
“A game show presents contestants with four doors: behind one of the doors is a car worth $1,000; behind another is a forfeit whereby the contestant must pay $1,000 out of their winnings thus far on the show. Behind the other two doors there is nothing.
The order of the game is as below:
1. The contestant chooses one of four doors.
2.The game show host opens another door; revealing that there is ‘nothing’ behind it.
3. The contestant is given the option of changing their choice to one of the two remaining unopened doors.
4. The contestant’s final choice door is opened, either to their delight (a car!), dismay (a penalty), or indifference (nothing).
a. The contestant wants to maximise their expected wealth.
b. The contestant is risk averse.
What is the optimal strategy for the contestant?”