[Open Yale Courses –> ECON 159 Game Theory]
[Transcript: Putting yourselves into other people’s shoes]
The formal parts of a game:
1. Players
2. strategies set
3. payoffs
Here is a question:
"Without showing your neighbor what you are doing, put it in the box below a whole number between 1 and a 100. We will (and in fact have) calculated the average number chosen in the class and the winner of this game is the person who gets closest to two-thirds times the average number. They will win five dollars minus the difference in pennies."
Here is the analytic process:
1. no one is going to choose a strategy bigger than 67 (dominated strategy: 67 and above) [Rational myself; Know others are Rational]
2. That all strategies 45 and above are hence also rules out (45-67 are dominated once we delete the 67 and above) (These strategies are NOT dominated in the original game, but they are weakly dominated once we delete 68 through 100) —- ‘in shoes’ argument [R, KR, KKR]
3. rule out the strategies from 30 through 45 —-’in shoes in shoes’ argument [R, KR, KKR, KKKR]
4. rule out the strategies from 20 through 30 —-’in shoes in shoes in shoes’ argument [R, KR, KKR, KKKR, KKKKR]
……
common knowledge: "I know something, you know it, you know that I know it, I know that you know it, I know that you know that I know it, etc.etc. : an infinite sequence"
5. If we had common knowledge of rationality in this class, then the optimal choice would have been 1.
6. It turns out that the average in this class, the average choice was about 13, which means two-thirds of the average was 9.
7. You also need to put yourself into other people’s shoes and think about how sophisticated are they at playing games. And you need to think about how sophisticated do they think you are at playing games.
common knowledge ≠ mutual knowledge
common knowledge is a statement about not just what I know, it’s about what do I know the other person knows that I know that the other person…
