課程名稱︰賽局論
課程性質︰大學部選修
課程教師︰古慧雯
開課系所︰經濟系
考試時間︰2006.03.06 星期一下午1:20~2:00
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
總分十分.
1.Please reconsider the voting game we introduced in the first week. 3 club
members, Boris, Horace and Maurice consider whether to admit Alice, Bob or
nobody into their club. In the first round vote, ther will decide whether to
puruse Alice or Bob's case. If the majority of members prefer to dicuss
Alice's (Bob's) case, they will then turn to vote whether to admit Alice
(Bob) in or to admit nobody in.
The following table shows their preference ordering. The top (bottom) one is
the most (least) preferable result.
───────────────────────
Boris Horace Maurice
───────────────────────
Alice nobody Bob
nobody Alice Alice
Bob Bob nobody
────────────────────────
Everybody knows everybody else's preference. Please consider the subgame
perfect equilibrium of the voting game to answer the following question.
(a) (1 point) If in the second round, they have to discuss whether to admit
Alice or nobody, how will Boris vote in this last round?
(b) (1 point) If in the second round, they have to discuss whether to admit
Bob or nobody, how will Boris votw in this last round?
(c) (2 points) Will Boris vote for Alice or Bob in the first round? Why?
2.K is the knowledge operator. P is the possibility operator, and PE = ~K~E.
Consider the following axioms.
(K0) KΩ = Ω
(K1) KE 包含於 E
(K2) K(E∩F) = KE∩KF
(K3) KE 包含於 KKE
(K4) PE 包含於 KPE
Please use these 5 axioms to prove the following. State clearly which axiom
you need for the proof.
(a) (2 points) K(空集合) = 空集合
(b) (2 points) KE 包含於 K(E∪F)
(c) (2 points) If E and F are truisms, then E∪F is a truism.
Game12.ctx
※ 編輯: greensunlife 來自: 140.112.250.104 (07/01 18:54)