推 gin22135 :哀~真想知道全班平均是幾分XD 安慰一下自己 05/26 02:01
課程名稱︰賽局論
課程性質︰選修
課程教師︰古慧雯
開課學院：社科院
開課系所︰經濟系
考試日期（年月日）︰101.05.11
考試時限（分鐘）：10:20-11:30 (70mins)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.Consider the following game. The first (second) element of the payoff vector
is the payoff to the row (column) player.
│ slow│ speed
───┼───┼───
slow│ 2,2│ 0,3
───┼───┼───
speed│ 3,0│ -1,-1
(a)(3 points) Find out all the Nash equilibrium.
(b)(5 points) Consider this game to be repeated twice. Find 3 subgame
perfect equilibrium which yield an expected patoff of 3 to each player.
2.(10 points) Consider the simplified Parchessi game of section 3.8.1 (as
attached) with the modification that, when a counter is exactly one square
from the winning square, then only the throw of a tail permits it to be
advanced. Other rules remain unchanged. Positions 1 and 2 of figure 3.17 no
longer have the value 1. Let their values be g and h respectively. Prove
that d < g.
3.Consider a two person zero-sum game with a payoff matrix M which specifies
the payoff to the row player. Let [m lower bar] ([m bar]) denote the row
(column) player's security level when both players consider to use only pure
strategies, and let [v lower bar] ([v bar]) denote the row (column) player's
security level when both players consider to use mixed strategies.
(a)(4 points) Please compare [m lower bar] and [v lower bar.] (Give the
mathematical forms of [m lower bar] and [v lower bar,] and analyze their
their difference rigorously.)
(b)(3 points) Suppose [m lower bar] = [m bar.] Prove that the row player's
security level is [m lower bar] when both players consider to use mixed
strategies. (You could quote the result that [v bar] > [v lower bar.]
Other than that any claim has to be provided with a detailed proof.)
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