In a nutshell
Key Ideas
Notes
Bathroom needs to be cleaned
No one wants to do it. If someone does it, both get a utility of 1 If no one does it, no one gets a utility Whoever does it incurs a cost
| Y | N | |
| Y | 1-c1, 1-c2 | 1-c1, 1 |
| N | 1, 1-c2 | 0,0 |
A better example: Someone needs to call the electric company
Cost structure
- For player 1
- 1-c1 is known
- c1 < 1/2
- c1 is common knowledge
- For player 2
- c2 is low with probability < 1/2
- c2 is high with probability 1-p
- cost is more than ‘1’ (where 1 is the reward for the task)
- Exact value of c2 is only known to player 2
Intuition
|P1|P2|u1|u2| ————- |X|X|+ve|eventually -ve| |X| |+ve|1| | |X|1|eventually -ve| | | |0|0|
More rigorous treatment
u2(s1, N|h) = 1-l >= 0
u2(s1, Y|h) = 1-h < 0
lemma 1: If c2=h -> s2(h)=N
u1(s2, Y) = 1-c1 > 1/2
u1(s2, N) = p*u1(s2(l), N) + (1-p)*u1(s2(h), N) = p*u1(s2(l), N) <= p*1 = p < 1/2
lemma 2: In BNE, player 1 plays Y
When P2’s type is l, they will still choose N.
Topic 1
Misc
- It’s best to be more vocal about your procrastination / make it seem like you are less likely to do something than you actually would