Open Yale Course -- 《博弈论》Problem Set 1 (求对答案)

1Strategy a strictly dominates strategy b, if payoff from a is strictly greater than that from b, regardless of what others do.
Strategy a weakly dominates strategy b, if payoff from a is greater or at least equal as that from b, regardless of what others do.
   l c r
T 3,1 3,1 3,1
M 1,0 2,2 1,3
D 1,3 2,2 2,2
M is strictly dominated by T
c is weakly (but not strictly) dominated by r
2a. No strict, but have weakly dominated strategies. c is WDed by r, M is WDed by D
2b. after deleting c and M, r is WDed by l, D is WDed by T. after deleting r and D, only (T,l) left.
2c. if not deleting WDed strategies, the NE shall be top right(T,r) and down left(D,l), But after deleting WDed strategies, the only choice is (T,l) which is not NE.
3a. s3,4,5,6,7,8,9 all SD s1
3b. s1 is SDed by s2 as well as by s3..s9. In reduced game, s2 is SDed by s3 as well as s4...s8
4a. For member 1, c is WDed by a;
For member 2, b is WDed by c ?
For member 3, a is WDed by b ?
4b. In reduce game, For member 1, b is WDed by a, so a is his choice
For member 2, a is WDed by c, so c is his choice
For member 3, no dominated, but the best response to the above is to choose c.
And the final winner is c.