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Answers to Odd-Numbered Problems,4th Edition of Games and Information, Rasmun
Eric Rasmun,Indiana University School of Business,Rm.456,1309E10th Street, Bloomington,Indiana,47405-1701.Office:(812)855-9219.Fax:812-855-3354.Eras-mu@Indiana.edu./GI
PROBLEMS FOR CHAPTER4
October15,2009Erasmu@indiana.edu.Http://
PROBLEMS FOR CHAPTER4
4.1.Repeated Entry Deterrence
Consider two repetitions without discounting of the game Entry Deterrence I from Section 4.2.Assume that there is one entrant,who quentially decides whether to enter two markets that have the same incumbent.
(a)Draw the extensive form of this game.
Answer.See Figure A4.1.If the entrant does not enter,the incumbent’s respon to entry in that period is unimportant.
Figure A4.1:Repeated Entry Deterrence
(b)What are the16elements of the strategy ts of the entrant?
Answer.The entrant makes a binary decision at four nodes,so his strategy must have four components,strictly speaking,and the number of possible arrangements is
(2)(2)(2)(2)=16.Table A4.1shows the strategy space,with E for Enter and S for
Stay out.
Table A4.1:The Entrant’s Strategy Set
Strategy E1E2E3E4
1E E E E
2E E E E
3E E E S
4E E S S
5E S S S
6E S E E
7E S S E
8E S E S
9S E E E
10S S E E
11S S S E孔雀画
12S S S S
13S E S S
14S E S E
15S E E S
请示报告的格式及范文
16S S E S
Usually modellers are not so careful.Table A4.1includes action rules for the Entrant to follow at node
s that cannot be reached unless the Entrant trembles,somehow deviating from its own strategy.If the Entrant choos Strategy16,for example, nodes E3and E4cannot possibly be reached,even if the Incumbent deviates,so one might think that the parts of the strategy dealing with tho nodes are unimportant. Table A4.2removes the unimportant parts of the strategy,and Table A4.3condens the strategy t down to its six importantly distinct strategies.
兔子怎么过冬
Table A4.2:The Entrant’s Strategy Set,Abridged Version I
Strategy E1E2E3E4
1E-E E
2E-E E
3E-E S
4E-S S
5E-S S
6E-E E
7E-S E
8E-E S
9S E--
10S S--
广东科学馆11S S--
小白兔养成记12S S--
13S E--
14S E--
15S E--
16S S--
Table A4.3:The Entrant’s Strategy Set,Abridged Version II风筝的英语
Strategy E1E2E3E4
1E-E E
3E-E S
4E-S S
7E-S E
9S E--
10S S--
(c)What is the subgame perfect equilibrium?
Answer.The entrant always enters and the incumbent always colludes.
(d)What is one of the nonperfect Nash equilibria?
Answer.The entrant stays out in thefirst period,and enters in the cond period.
钢琴属于什么乐器The incumbentfights any entry that might occur in thefirst period,and colludes in the cond period.
4.3.Heresthetics in Pliny and the Freedmens’Trial(Pliny,1963,pp.221-4,Riker, 1986,pp.78-88)
Afranius Dexter died mysteriously,perhaps dead by his own hand,perhaps killed by his freedmen(rvants a step above slaves),or perhaps killed by his freedmen by his own orders.The freedmen went on trial before the Roman Senate.Assume that45percent of the nators favor acquittal,35percent favor banishment,and20percent favor execution,
and that the preference rankings in the three groups are A B E,B A E,and E B A.Also assume that each group has a leader and votes as a bloc.
(a)Modern legal procedure requires the court to decide guiltfirst and then assign a
penalty if the accud is found guilty.Draw a tree to reprent the quence of events (this will not be a game tree,since it will reprent the actions of groups of players, not of individuals).What is the outcome in a perfect equilibrium?舍不得分开的句子
Answer.Guilt would win in thefirst round by a vote of55to45,and banishment would win in the cond by80to20.See Figure A4.2.Note that Figure A4.2is not really an extensive form,since each node indic
ates a time when many players make their choices,not one,and the numbers at the end are not payoffs.
Figure A4.2:Modern Legal Procedure
(b)Suppo that the acquittal bloc can pre-commit to how they will vote in the cond
round if guilt wins in thefirst round.What will they do,and what will happen?
What would the execution bloc do if they could control the cond-period vote of the acquittal bloc?
Answer.The acquittal bloc would commit to execution,inducing the Banishment bloc to vote for Acquittal in thefirst round,and acquittal would win.The execution bloc would order the acquittal bloc to choo banishment in the cond round to avoid making the banishment bloc switch to acquittal.
