課程名稱︰賽局論
課程性質︰選修
課程教師︰古慧雯
開課系所︰經濟系
考試時間︰95.06.26
是否需發放獎勵金：是，謝謝
（如未明確表示，則不予發放）
試題 :
1.Consider the following normal form game:
│ S1 S2 S3
────────────────
S1│0.5,0.5 1,-1 -1,1
S2│ -1,1 0.5,0.5 1,-1
S3│ 1,-1 -1,1 0.5,0.5
(a) Is there any pure strategy Nash equilibrium? If there is, what is it?
(b) Is there any mixed strategy Nash equilibrium? If there is, what is it?
(c) Is there any evolutionary stable strategy in this game? If there is, what
is it?
2.Consider the following game:
│ C D
──────
C│3,3 0,4
D│4,0 1,1
(a) What is the Nash equilibrium?
(b) What is the Nash equilibrium, if the game is repeated 10 times?
3.Consider the following game:
│ C D E
──────────
C│3,3 0,4 0,0
D│4,0 1,1 0,0
E│0,0 0,0 0.5,0.5
(a) Please find all the pure strategy Nash equilibrium.
(b) Suppose the game is repeated 10 times, and each player cares about the sum
of his/her payoffs. Is there any Nash equilibrium in which (C,C) will be
played in some periods?
4.Odd Man Out is a 3-player, zero-sum game. Each of 3 risk-neutral players
simultaneously chooses heads or tails. If all make the same choice, no money
changes hands. If one player chooses differently from the others, he must
pay the others one dollar each.
(a) What is a security strategy for a player? (The way how you approach this
problem is important. No point is granted to a correct guess.)
(b) Is it a Nash equilibrium when each player plays his security strategy?
(c) In this game, is a Nash equilibrium necessarily a profile consisting of 3
players's security strategies?
5.Draw the cooperative payoff region X for following the bimatrix game when
the players can make binding agreements to use a lottery, but cannot freely
dispose of utils nor transfer them. Then find the value of regular Nash bar-
gaining solution, when the disagreement point is (0,1).
│ t1 t2 t3
──────────
s1│-1,-1 1,3 3,0
s2│ 1,0 0,1 0,3
6.Consider a dynamic system of pi(t), i=1,2,3. The system satisfies the
following equations:
p'1/p1 = p2-p3
p'2/p2 = p3-p1
p'3/p3 = p1-p2
Besides,
p1(t)+p2(t)+p3(t)=1, for all t.
(a) What is the rest point of this system?
(b) Prove that if p1(0)p2(0)p3(0) = c then p1(t)p2(t)p3(t) = c, for all t>0
(c) Is there any asymptotic attractor in this system?
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◆ From: 140.112.242.73
※ 編輯: knom 來自: 140.112.242.73 (06/27 10:07)