[考試] 混合策略Nash均衡一問
來源:104年度台大研究所
科目:個體經濟學
問題:
複選題
Consider the normal form bellow. Suppose the row player uses a mixed
strategy and choose s1 with probability p, and the column player uses
a mixed strategy and choose t1 with probability q and t2 with
probability r. In a Nash equilibrium with the mixed strategies,
how will these two players play the game?
t1 t2 t3
s1 (1,2) (4 ,3) (2,1)
s2 (3,2) (-1,1) (0,0)
(A)p=1/3
(B)p=1/2
(C)q+r=1
(D)q=2/7
(E)q=5/7
我的想法:
我原本打算用極大化報酬的方式找出p、q和r，以下是我的計算過程:
Maxπrow = p*(1q+4r+2(1-q-r))+(1-p)*(3q-1r)
一階微分等於0得:-4q+3r+2=0
Maxπcolumn = q*(2p+2(1-p))+r*(3p+1(1-p))+(1-q-r)*(1p)
對q微分並令它等於0得:p=2
對r微分並令它等於0得:p=-1
得到的這兩個p都超怪的，但我已經算過很多遍了，每次都這樣。所以小弟想請問:
1.這樣的求解方向有錯嗎?
2.若無，請問是計算方式出了問題嗎?
拜託各位大大幫忙了，謝謝~~
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