Math 486.
Game
Theory. Miderm 3. Dec.3, 2009.
Name______________________________________
Find the equilibria in pure strategies, the Pareto optimal solutions
in pure
strategies,
the characteristic function, the Nash bargaining solution, and
the Shapley
values.
1 (30 pts). Players: the row player Ann; the column
player Bob.
|
0, 1 |
1, 0 |
0, 0 |
1, 1 |
|
1, 1 |
1, 3 |
2, 4 |
2, 2 |
|
0, 3 |
0, 0 |
1, 3 |
3, 2 |
|
1, 0 |
0, 0 |
0, 0 |
1, 4 |
(payoffs for Ann and Bob)
2 (45 pts). Players: A, B, C
strategies
payoffs
1 1
1
0 1 2
1 1
2
1 0 1
1 2
1
2 3 3
1 2
2
1 2 3
2 1
1
0 0 1
2 1
2
1 1 1
2 2
1
2 3 3
2 2
2
2 3 2
3 1
1
0 0 0
3 1
2
0 0 0
3 2
1
1 1 1
3 2
2
2 4 0