1. Consider a homeowner with Von-Neumann and Morgenstern utility function u, where u (x) = 1 - e-x for wealth level x, measured in million US dollars. His entire wealth is his house. The value of a house is 1 (million US dollars), but the house can be destroyed by a flood, reducing its value to 0, with probability π ∈ (0, 1). What is the largest premium P is the homeowner is willing to pay for a full insurance? (He pays the premium P and gets back 1 in case of a flood, making his wealth 1 - P regardless of the flood.)
2. Consider the following game
| |
a |
b |
c |
d |
| w |
2,0
|
0,5
|
1,0
|
0,4
|
| x |
4,1
|
2,1
|
0,2
|
1,0
|
| y |
2,1
|
5,0
|
0,0
|
0,3
|
| z |
0,0
|
1,0
|
4,1
|
0,0
|
(a) Find all Nash Equilibrium
3. Find all pure and mixed strategy Nash Equilibriums in the following games.
|
|
L R
|
|
R
|
|
A
|
2, 0
|
2, 0
|
A
|
2,0
|
2, 0
|
|
B
|
3, 0
|
0, 1
|
B
|
5, 0
|
0, 3
|
|
C
|
0,1
|
3, 0
|
C
|
0,2
|
5, 0
|
4. Consider the following extensive form game
(a) List the strategies available to each player in the game
(b) Construct payoffs (a, b, c, d, e, f, g, h, i, j, k, l) such that the terminal node r3, with payoffs (k, l), will be the unique backwards-induction outcome.