Math 486. Febr. 4, 2010. Midterm
1.
5 problems, 15 pts each.
Name____________________
m1 ..... /75. total
................./.....
Write your name on the class list and on every page you submit. Return this page.
Find an equilibrium in pure strategies and the corresponding
payoff. In Problems 1 and 2, the bet is $1.
1. Restricted Nim. Last move wins. Players alternate
and can take 1,2,4, or 5 stones in a move from a pile. Initial position: 2
piles, 100 and 200 stones.
2. Blackjack. Player (P) has hard 17. Dealer (D) shows 10. Cards remaining including D's face-down are 4, 4,4, 7, 7,7.
3. 2 player game in normal form.
|
7, 1 |
4,0 |
-1, 3 |
0,0 |
3, 3 |
-3,4 |
|
5,-1 |
5,0 |
-2, 5 |
1, 4 |
3,1 |
0,0 |
|
0, 5 |
4,-1 |
-2, 4 |
6, 0 |
0, 3 |
1,1 |
|
1,1 |
5,0 |
0, 3 |
6,0 |
3,3 |
3,3 |
4. Extensive form, 3 players, A B, C.
initial position B
/
\
/
\
A
B
/
\
/ \
B
C
B C
/
\
/
\
/ \
/ \
1,2,3 0,-1,0 -1,-2,1
-1,0,1 2,-1,0 0,0,2
5. Game with 3 players, A, B, C. in
normal form.
strategy
payoff
A B C A
B C
1 1
1
0 -1 1
1 1
2
1 1 -2
1 2
1
1 0 0
1 2 2
0 0 1
2 1
1 0 -1 1
2 1
2
1 1 -2
2 2 1
1 0 -1
2 2 2 -1
1 0
3 1
1 0 -1 1
3 1 2
-1 1 -2
3 2
1
1 -1 0
3 2 2
-1 0 0