博弈论与策略思维课后练习

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博弈论与策略思维课后练习

博弈论与策略思维课后练习（点此刷新练习不同题目）判断题：1、萨缪尔森说，要把一只鹦鹉培养成一个经济学家，要告诉它三个词：供给，需求，纳什均衡[题号：Qhx008225]A、对B、错您的回答：B正确答案：B题目解析：萨缪尔森说，要把一只鹦鹉培养成一个经济学家，要告诉它两个词，即供给与需求；坎贝尔引申说，要把一只鹦鹉培养成一个现代经济学家，还要告诉它什么是纳什均衡。

2、在重复博弈中，合谋是纳什均衡。

[题号：Qhx008230]A、对B、错您的回答：B正确答案：B题目解析：重复博弈分为无限重复博弈与有限重复博弈，在无限重复博弈中，合谋是纳什均衡。

3、无限重复博弈会导致期末问题。

[题号：Qhx008235]A、对B、错您的回答：B正确答案：B题目解析：知道已知次数的有限重复博弈会导致期末问题。

4、协调博弈只有一个纳什均衡。

[题号：Qhx008229]A、对B、错您的回答：B正确答案：B题目解析：协调博弈中至少有两个纳什均衡，具体是哪个均衡组合，需要博弈方协调。

5、石头剪刀布是序列博弈。

[题号：Qhx008227]A、对B、错您的回答：B正确答案：B题目解析：石头剪刀布是同步博弈。

单选题：1、在智猪博弈模型中，（）是纳什均衡。

[题号：Qhx008242]A、大猪小猪都按B、大猪按小猪等C、小猪按大猪等D、小猪大猪都等您的回答：B正确答案：B题目解析：智猪博弈主要用来分析处于弱势地位的参与者与强势地位的参与者博弈时的相处之道，在该博弈中，小猪搭大猪便车显示出了博弈智慧，大猪按小猪等为纳什均衡。

2、在无限重复博弈的情况下，可达成最终合作的策略是（）。

[题号：Qhx008247]A、一报还一报B、冷酷策略C、触发策略D、劣策略您的回答：A正确答案：A题目解析：在无限重复博弈情况下，无论是根据计算机模拟还是实际的计算，在存在一报还一报的触发策略的情况下，可以达成合作。

3、将博弈论由静态向动态的扩展，建立了“子博弈精练纳什均衡”概念的经济学家是（）。

博弈论指定习题和参考答案

指定习题和参考答案Chapter 2: 1, 21. (a) D. There is so much amount and kinds of yogurt that each shopper need not consider whatothers do.(b) G. A prom is likely to be small enough that any participant can have some conceivable influence on others. For example, these two should prevent from dressing the same. However, in a BIG CITY, this may not be a case.(c) D. If he is not restricted to any specific university.(d) G. There are so few competitors for this specific product.(e) G. He must consider the interaction between him and his running mate. Even more, he must consider the response of the constituency when he chooses the mate.2. (a) Z; R/NR; I; F; NC.(b) NZ; NR; A; F; C.(c) NZ;NR; I; F; CChapter 3: 1, 2, 6, 71. (a) D=3, T=6(b) D=4, T=9(c) D=5, T=82. (a) #S(A)=2, S(A)={N,S}; #S(B)=2, S(B)={t, b}(b) #S(A)=2*2*2=8, S(A)={NNN, NNS, NSN, NSS, SNN, SNS, SSN, SSS}(left, right-up,right-down)#S(B)=2, S(B)={t, b}; #S(C)=2, S(C)={u,d}(c) #S(A)=2*2*2=8, S(A)= {NNN, NNS, NSN, NSS, SNN, SNS, SSN, SSS}(left, middle,right)#S(B)=8, S(B)={nnn, nns, nsn, nss, snn, sns, ssn, sss}6. (a) At the final run, B must take dimes. At the run next to final, if A choose to pass, given Btake dime at the final run, he can only get the reward accumulating at a speed of 5 cents per turn, initially 0 cents. If he takes dimes, he gets the dimes accumulating at a speed of 20 cents per turn, initially 10 cents. He surely takes dimes. Given this, B must take dimes at the run second next to final (B’s payoffs are the same as in our initial game) . Then A has the same reasoning as at the next to final run. And so on. So the rollback equilibrium strategy is always taking dime, for both players.(b) Using rollback method, let’s consider from the second round.No matter what payoffs both have got in the first round, they have sunk and cannot affect both players’ decisions in the second round. So two players play the second round as if it is a single-round centipede. So each plays is always choosing to take dimes, resulting payoffs of10 to A and 0 to B.Keeping this in both players’ mind, the first round is played almost as a single-roundcentipede, except that A always gets a reward of 10, whether she passes the dime or take it.But the fact that you always get something will neither affect your decision. So finally the first round game is exactly as a single-round centipede.Use rollback to this reduced single-round centipede. Notice the game is essential the same as before in the first 6 runs when the total amount is not accumulated to 50 when it’s player A’ s turn to play. If we can decide that the game after the 6th run will have an equilibrium of both players always taking dimes, we can be sure that B will get at most 20 when the 7th run comes and A (at most) takes 50.Now consider this ‘small’ equilibrium with only the last 4 runs. B will take dimes at in the final run (with a payoff of 90, otherwise 0). In any round before for A to play, taking dimes will leave her at least 50, but passing it will leave her at most 100-90=10 if B takes dimes then. In any round before for B, taking dime will leave him at least 60, but passing it will leave her at most 100-50=50 if A takes dimes then. Given the final run’s action of B (taking dimes), we can derive that both will always take dime in any round before, but after 6th run.Now let’s go back to our 6th run. B will take dimes at the 6th run (with a payoff of 60, otherwise 20). Given B’s choice, the game before the 6th run goes like the original one.The equilibrium is that both players always take dimes.(c) All the logic of (b) applies here until we begin to consider the last 5 runs (not 4 runs at thistime) of the first round game. Use rollback.B takes dimes in the final run, but get only 40 and leave 50 (as we restricts) to A. In the9th(second to the last) run, A can choose either to pass or take dimes(getting 50 both). The game essential the same when it ends in 9th run or 10th run.However, the 8th run is crucial. B can choose either to pass or to take dimes (getting 40 both). If B chooses to take dimes, A will definitely chooses to take dimes in the 7th run, and so on. The cooperation totally breaks and results in taking dimes always (our old equilibrium outcome).In any round before, but after 5th run, if both expect complete cooperation throughout the future, then they can either choose to pass or take. Any single deviation from cooperation (taking dimes) will result in total breakdown. So the 6-8th runs are all crucial points, given cooperation afterwards.Consider both pass dimes. Given this, at the 5th run, A chooses to pass is at least as good as to take. Taking them leads to breakdown as well. Suppose she passes it. B will also be indifferent with passing or taking dimes. So the 4-5th runs are also crucial points.However the 3rd run and the earlier are not crucial. If cooperation always happens afterward, passing dimes are always strictly better than taking dimes. If breakdown has already happen afterwards, taking dimes are definitely better choices.Summary: this game has multiple equilibria. Always passing dimes is one of them. Any deviations in one of 4-8th runs, given cooperation afterwards, will lead to breakdown from the very beginning. ( The number of equilbria is (1+5)*2=12, taking into account in the 9th run, both passing or taking dimes are indifferent for A.)7. (a) Amy; Beth.The player who reaches exactly 89 first will win; thus the player who reaches 78 first will win;thus 67,56, 45, 34, 23, 12, 1. Obviously Amy will reach 1 first.The player who reaches exactly 99 first will win. Then 88, 77, 66, 55, 44, 33, 22, 11.Obviously Beth will reach 11 first.(b) For Amy: 1 in the first run, then 11 no matter what Beth chooses, and 22, and so on. ForBeth, she can choose any amount between 1 and10.For Amy: any amount between 1 and 10. For Beth, 11 in his first run, 22 in his second run, and so on.Chapter 4: 2(d), 3(d), 5, 6, 9, 122. (d) Up is dominated by Straight (for Row). Then Left and Middle are both dominated by Right(for Column). Given Column plays Right, Row chooses Straight. The only NE is (Straight, Right).3. (d) (North, East) (unique NE). No dominant or dominated for both. Best-response analysis.5. Dominance solvable. (Up, Left). (Level, Center) has the same payoffs but not NE. There arealso other strategy configurations having strictly higher payoffs but not NEs.6. (1)JapaneseNorthern Southern AmericanNorthern 2 2Southern 1 3 (2) “Southern” is weakly dominated by “Northern” for Japanese. (North, North) is the only NE.(Check if “Southern” for Japanese can be part of any NE before you eliminate it.)9. (a) 3 NEs: (1, 1), (2, 2), (3, 3). The first is less likely to be focal point. But the other two areequally likely to be.(b) 12.5; Yes; Mixed strategy (just like flipping coins) can be used.12. (a) Two NEs: (Brunette, Blonde), and (Blonde, Brunette), yielding payoffs (5, 10) and (10, 5)respectively.Player 2Blonde BrunettePlayer 15Blonde 0,0 10,Brunette 5, 10 5, 5(b)Player 3Blonde BrunettePlayer 2 Player 2Blonde Brunette Blonde Brunette Player 1Blonde 0, 0, 0 0, 5, 0 0, 0, 5 10, 5, 5Brunette 5, 0, 0 5, 5, 10 5, 10, 5 5, 5, 53 NEs: (Blonde, Brunette, Brunette), (Brunette, Blonde, Brunette), and (Brunette, Brunette, Blonde), with payoffs 10 for who wins the Blonde, 5 for who wins Brunette.(c) The only possible NEs are those with only one pursues and wins the only Blonde and all others pursues and wins somehow excessive Brunettes.Or, follow the assumption given in text. Given k>=1, for any player, his payoffs of pursuing the Blonde is 0 and definitely worse than pursuing the Brunette with payoff 5. However, if k=0, you’d better pursue the Blonde.Consider this for a while, you will get the NE solutions.Thus All players choose Brunette cannot be a NE.。

博弈论各章节课后习题答案 (5)

第五章合作博弈1.设三人联盟博弈的特征函数v 的值是：v({i})=0,i=1,2,3;v({1,2})=2/3,v({1,3})=7/12,v({2,3})=1/2,v({1,2,3})=1。

求出该联盟博弈的核心，并用图形表示出来。

解：博弈G 的核心C(v)。

博弈G 的转归集I[N,v]为:123123123[,]{(,,)0,0,0,1}I N v x x x x x x x x x x ==≥≥≥++=若，则的充分条件为：],[),,(321v N I x x x x ∈=)(v C x ∈x 1≥0;x 2≥0;x 3≥0;x 1+x 2≥2/3;x 1+x 3≥7/12;x 2+x 3≥1/2;x 1+x 2+x 3=1由后面几个不等式得到x 1≤1/2;x 2≤5/12,x 3≤1/3.该联盟博弈的核心C(v)={(x 1,x 2,x 3)|0≤x 1≤1/2,0≤x 2≤5/12,0≤x 3≤1/3,x 1+x 2+x 3=1}核心C(v)是图中阴影区域（含边界）。

2.假设有一3人合作博弈，其特征函数为：v({1,2,3})=200,v({1,2})=150,v({1,3})=110,v({2,3})=20,v({1})=100,v({2})=10,v({3})=0。

计算该合作博弈的Shapley 值，核心，最小ε-核心，稳定集，内核和核仁。

1、Shapley 值φ1(v)＝1/3（100-0）＋1/6（150－10）＋1/6（110-0）＋1/3（200-20）＝135φ2(v)＝1/3（10-0）＋1/6（150－100）＋1/6（20-0）＋1/3（200-110）＝45φ3(v)＝1/3（0-0）＋1/6（20－10）＋1/6（110-100）＋1/3（200-150）＝20所以该博弈的Shapley 值φ(v)＝（135，45，20）2、博弈G 的核心C(v)。

博弈G 的转归集I[N,v]为:}200,0,10,100),,({],[321321321=++≥≥≥==x x x x x x x x x x v N I 若，则的充分条件为：],[),,(321v N I x x x x ∈=)(v C x ∈x 1≥100;x 2≥10;x 3≥0;x 1+x 2≥150;x 1+x 3≥110;x 2+x 3≥20;x 1+x 2+x 3＝200对此可作高为200的重心三角形Δ123。

博弈论战略分析入门课后练习题含答案

博弈论战略分析入门课后练习题含答案题目翻译：
1.两个人轮流选择从1到7之间的数字，不能重复选择，哪个人最后选
择7就赢了。

如果两个人都采用最优策略，第一个选择数字的人能否保证获胜？
2.有两个球队A和B，比赛规则为A队挑选一个数字k，B队猜测这个
数字是奇数还是偶数。

如果B队猜错了，A队获胜；反之，B队获胜。

如果A队更喜欢奇数，那么它们应该挑选多少奇数呢？
解答：
1.第一个选择数字的人不能保证获胜，因为第二个人可以选择数字4，
让第一个人面临两个选择：选择数字2或6。

无论哪个数字，第二个人都可以接下来选择数字3，然后赢得游戏。

所以第一个人不能获胜。

2.如果A队总是选择奇数，那么B队的最优策略是选择奇数。

因为如果
A队选择奇数，B队就获胜，如果A队选择偶数，B队有50%的机会猜对，平局的概率为25%，B队的总胜率为75%。

因此A队最好选择所有奇数，这样B 队只有50%的机会获胜。

思路解析：
1.对于第一道题，我们需要根据规则分析游戏的局面，然后确定最优策
略。

在此基础上，我们可以找到第一个人的必胜策略，或者证明无论如何第一个人都不能获胜。

2.对于第二道题，我们需要考虑两个球队的思考方式，并且理解如何最
小化选手的期望获胜率。

这也需要一些概率的基础知识。

以上就是本次博弈论战略分析入门课后练习题答案。

希望这些题目能够帮助您加深对博弈论和战略分析的理解，进一步提升您的分析能力和决策能力！
1。

博弈论课后习题答案

博弈论课后习题答案博弈论课后习题答案博弈论是一门研究决策和策略的学科，它涉及到多个参与者之间的相互作用和决策过程。

在博弈论的学习过程中，习题是非常重要的一部分，通过解答习题可以加深对博弈论概念和原理的理解。

下面是一些常见博弈论习题的答案，希望对大家的学习有所帮助。

1. 两人囚徒困境博弈在囚徒困境博弈中，两个囚犯被关押在不同的牢房里，检察官给每人提供了一个选择：合作（合作供认）或背叛（沉默）。

如果两人都合作，那么每个人的刑期都会较短；如果两人都背叛，那么每个人的刑期都会较长；如果一个人合作而另一个人背叛，那么背叛的人将会获得较短的刑期，而合作的人将会获得较长的刑期。

答案：在囚徒困境博弈中，每个囚犯都会追求自己的最大利益。

根据博弈论的原理，无论对方选择什么，背叛都是最优策略。

因此，两人都会选择背叛，最终导致双方都获得较长的刑期。

2. 石头剪刀布博弈石头剪刀布是一种常见的博弈游戏，两个参与者同时出示石头、剪刀或布，根据两者的选择，结果会有不同的得分。

答案：在石头剪刀布博弈中，每个参与者都有三种选择，而且每种选择的胜负关系都不同。

根据博弈论的原理，最优策略是随机选择，使得对手无法预测自己的选择。

这样做可以最大程度地减少对手的获胜概率。

3. 拍卖博弈拍卖是一种常见的博弈形式，参与者通过竞价来争夺一个物品或服务。

在拍卖中，不同的拍卖规则和策略会对结果产生影响。

答案：在拍卖博弈中，最常见的策略是以自己的估值为基准进行竞价。

如果一个参与者的估值高于其他参与者，那么他可以通过竞价来获得物品或服务。

然而，如果其他参与者也有较高的估值，那么竞价将会继续上升，直到只剩下一个竞价者。

在这种情况下，最高的竞价者将会获得物品或服务，但是他需要支付他的竞价。

4. 价格战博弈价格战是一种常见的博弈形式，不同的公司通过调整价格来争夺市场份额。

在价格战中，公司的利润和市场份额会受到价格策略的影响。

答案：在价格战博弈中，最优策略取决于对手的策略和市场需求。

博弈论课后习题答案

博弈论课后习题答案第四部分课后习题答案1. 参考答案:括号中的第一个数字代表乙的得益，第二个数字代表甲的得益，所以a表示乙的得益，而b表示甲的得益。

在第三阶段，如果，则乙会选择不打官司。

这时逆推回第二阶段，甲会选择a,0不分，因为分的得益2小于不分的得益4。

再逆推回第一阶段，乙肯定会选择不借，因为借的最终得益0比不借的最终得益1小。

在第三阶段，如果，则乙轮到选择的时候会选择打官司，此时双方得益是(a,b)。

a,0逆推回第二阶段，如果，则甲在第二阶段仍然选择不分，这时双方得益为(a,b)。

b,2在这种情况下再逆推回第一阶段，那么当时乙会选择不借，双方得益(1，0)，当a,1时乙肯定会选择借，最后双方得益为(a,b)。

在第二阶段如果，则甲会选择a,1b,2分，此时双方得益为(2，2)。

再逆推回第一阶段，乙肯定会选择借，因为借的得益2大于不借的得益1，最后双方的得益(2，2)。

根据上述分析我们可以看出，该博弈比较明确可以预测的结果有这样几种情况:(1)，此时本博弈的结果是乙在第一阶段不愿意借给对方，结束博弈，双方a,0得益(1，0)，不管这时候b的值是多少;(2)，此时博弈的结果仍然012,,,ab且是乙在第一阶段选择不借，结束博弈，双方得益(1，0);(3)，此时博ab,,12且弈的结果是乙在第一阶段选择借，甲在第二阶段选择不分，乙在第三阶段选择打，最后结果是双方得益(a,b);(4)，此时乙在第一阶段会选择借，甲在第二阶段会选择分，ab,,02且双方得益(2，2)。

要本博弈的“威胁”，即“打”是可信的，条件是。

要本博弈的“承诺”，即a,0“分”是可信的，条件是且。

a,0b,2注意上面的讨论中没有考虑a=0、a=1、b=2的几种情况，因为这些时候博弈方的选择很难用理论方法确定和预测。

不过最终的结果并不会超出上面给出的范围。

2. 参考答案:静态贝叶斯博弈中博弈方的一个策略是他们针对自己各种可能的类型如何作相应的完整计划。

智慧树知到《博弈策略与完美思维》章节测试答案

智慧树知到《博弈策略与完美思维》章节测试答案第一章1、博弈论中，参与人从一个博弈中得到的结果常被称为（）。

A:效果B:支付C:决策D:利润正确答案：支付2、根据博弈的参与人之间是否达成具有约束力的契约来分,博弈可分为（）。

A:静态博弈和动态博弈B:合作博弈和非合作博弈C:完全信息博弈和不完全信息博弈D:完全信息静态博弈和完全信息动态博弈正确答案：合作博弈和非合作博弈3、和威廉·维克瑞共同分享1996年诺贝尔经济学奖的是（）。

A:泽尔腾B:谢林C:詹姆斯·莫里斯D:保罗·萨缪尔森正确答案：詹姆斯·莫里斯4、每一个参与者对所有其他参与人的特征、策略空间和支付函数有准确的认识，这样的博弈为（）。

A:动态博弈B:合作博弈C:常和博弈D:完全信息博弈正确答案：完全信息博弈5、博弈的关键要素包括（）。

A:战略B:参与人C:信息D:支付正确答案：战略,参与人,信息,支付第二章1、在具有占优战略均衡的囚徒困境博弈中（）。

A:只有一个囚徒会坦白B:两个囚徒都没有坦白C:两个囚徒都会坦白D:任何坦白都被法庭否决了正确答案：两个囚徒都会坦白2、严格劣战略是指参与人的某一个战略（）。

A:相对于本人其他所有战略，得分都是较低的B:相对于本人某个战略，得分是较低的C:相对于对手所有战略，得分都是较低的D:相对于对手某个战略，得分都是较低的正确答案：相对于本人某个战略，得分是较低的3、下列关于古诺模型的假设，说法正确的是（）。

A:某产品市场上仅有两家企业，高进入壁垒阻止了其他企业进入B:两家企业生产不同价格的产品C:总成本等于0D:两家企业同时进入市场，就价格制定进行博弈正确答案：某产品市场上仅有两家企业，高进入壁垒阻止了其他企业进入4、下列说法正确的是（）。

A:纳什均衡一定是占优策略均衡B:占优策略均衡一定是纳什均衡C:每个有限博弈都没有混合战略纳什均衡D:每个有限博弈都有混合战略纳什均衡正确答案：占优策略均衡一定是纳什均衡5、一个博弈如果有多个纳什均衡，我们一般如何来实现某个具体的纳什均衡？A:帕累托上策均衡B:风险上策均衡C:聚点均衡D:相关均衡正确答案：帕累托上策均衡,风险上策均衡,聚点均衡,相关均衡第三章1、下列描述哪个是正确的 ( )。

[新版]博弈论课后习题

第一章导论1、什么是博弈？博弈论的主要研究内容是什么？2、设定一个博弈模型必须确定哪几个方面？3、举出烟草、餐饮、股市、房地产、广告、电视等行业的竞争中策略相互依存的例子。

4、“囚徒的困境”的内在根源是什么？举出现实中囚徒的困境的具体例子。

5、博弈有哪些分类方法，有哪些主要的类型？6、你正在考虑是否投资100万元开设一家饭店。

假设情况是这样的：你决定开，则0.35的概率你讲收益300万元（包括投资），而0.65的概率你将全部亏损；如果你不开，则你能保住本钱但也不会有利润，请你（a）用得益矩阵和扩展形式表示该博弈；（b）如果你是风险中性的，你会怎样选择？（c）如果你是风险规避的，且期望得益的折扣系数为0.9，你的策略选择是什么？(d)如果你是风险偏好的，期望得益折算系数为1.2，你的选择又是什么？7、一逃犯从关押他的监狱中逃走，一看守奉命追捕。

如果逃犯逃跑有两条可选择的路线，看守只要追捕方向正确就一定能抓住逃犯。

逃犯逃脱可以少坐10年牢，但一旦被抓住则要加刑10年；看守抓住逃犯能得到1000元奖金。

请分别用得益矩阵和扩展形式表示该博弈，并作简单分析。

第二章完全信息静态博弈1、上策均衡、严格下策反复消去法和纳什均衡相互之间的关系是什么？2、为什么说纳什均衡是博弈分析中最重要的概念？3、找出现实经济或生活中可以用帕累托上策均衡、风险上策均衡分析的例子。

4、多重纳什均衡是否会影响纳什均衡的一致预测性质，对博弈分析有什么不利影响？5、下面的得益矩阵表示两博弈方之间的一个静态博弈。

该博弈有没有纯策略纳什均衡？博弈的结果是什么？6、求出下图中得益矩阵所表示的博弈中的混合策略纳什均衡。

7、博弈方1和2就如何分10 000元进行讨价还价。

假设确定了以下规则：双方同时提出自己要求的数额S1和S2，,如果s1+s2≤10 000，则两博弈方的要求都得到满足，即分别得到s1和s2，但如果是s1+s2＞10 000,则该笔钱就被没收。

博弈论各章节课后习题答案 (2)

（1）
( q1*, q*2,⋯, q*n )组成该博弈的纯策略纳什均衡点。
2
∑ 式（1）两边同时求和，可得：
n
q*i
=
Q*
=
n(a
−
c
−
Q* )
，于是
Q*
=
n (a n +1
−
c)
，
i =1
q*
=
a
−c
−
Q*
=
a−c n +1
，此时
p*=a-Q*=
a + nc n +1
，当
n
趋于无群大时，有
Q*=a-c,
(aij + d)x*i y j 是成立的 , 此即为 XA2Y* ≤ X*A2Y* ≤ X*A2Y 。所以
i =1 j=1
i =1 j=1
(X*,Y*)是矩阵博弈 G2 的纳什均衡点,并且
mn
mn
∑ ∑ ∑ ∑ v(G2) =
(a ij
+
d)x
* i
y*j
=
aijx*i y*j + d = v(G1) + d
第二章完全信息的静态博弈和纳什均衡
1. 什么是纳什均衡? （见教材）
2. 剔除以下规范式博弈中的严格劣策略，再求出纯策略纳什均衡。
先剔除甲的严格劣策略 3,再剔除乙的严格劣策略 2,得如下矩阵博弈。然后用划线法求出该矩
阵博弈的纯策略 Nash 均衡。
乙
甲
1
3
1
2,0 4,2
2
3,4 2,3
3. 求出下面博弈的纳什均衡。
该博弈的纳什均衡为下图的线段 AB：即：s1+s2=100,s1,s2∈[0,100]。

博弈论课后习题

第一章导论1、什么是博弈博弈论的主要研究内容是什么2、设定一个博弈模型必须确定哪几个方面3、举出烟草、餐饮、股市、房地产、广告、电视等行业的竞争中策略相互依存的例子。

4、“囚徒的困境”的内在根源是什么举出现实中囚徒的困境的具体例子。

5、博弈有哪些分类方法，有哪些主要的类型6、你正在考虑是否投资100万元开设一家饭店。

假设情况是这样的：你决定开，则的概率你讲收益300万元（包括投资），而的概率你将全部亏损；如果你不开，则你能保住本钱但也不会有利润，请你（a）用得益矩阵和扩展形式表示该博弈；（b）如果你是风险中性的，你会怎样选择（c）如果你是风险规避的，且期望得益的折扣系数为，你的策略选择是什么(d)如果你是风险偏好的，期望得益折算系数为，你的选择又是什么7、一逃犯从关押他的监狱中逃走，一看守奉命追捕。

如果逃犯逃跑有两条可选择的路线，看守只要追捕方向正确就一定能抓住逃犯。

逃犯逃脱可以少坐10年牢，但一旦被抓住则要加刑10年；看守抓住逃犯能得到1000元奖金。

请分别用得益矩阵和扩展形式表示该博弈，并作简单分析。

第二章完全信息静态博弈1、上策均衡、严格下策反复消去法和纳什均衡相互之间的关系是什么2、为什么说纳什均衡是博弈分析中最重要的概念3、找出现实经济或生活中可以用帕累托上策均衡、风险上策均衡分析的例子。

4、多重纳什均衡是否会影响纳什均衡的一致预测性质，对博弈分析有什么不利影响5、下面的得益矩阵表示两博弈方之间的一个静态博弈。

该博弈有没有纯策略纳什均衡博弈的结果是什么6、求出下图中得益矩阵所表示的博弈中的混合策略纳什均衡。

7、博弈方1和2就如何分10 000元进行讨价还价。

假设确定了以下规则：双方同时提出自己要求的数额S1和S2，0≤s1,s2≤10000,如果s1+s2≤10 000，则两博弈方的要求都得到满足，即分别得到s1和s2，但如果是s1+s2＞10 000,则该笔钱就被没收。

问该博弈的纯策略纳什均衡是什么如果你是其中一个博弈方，你会要求什么数额，为什么8、设古诺模型中有n家厂商、qi 为厂商i的产量，Q=q1+…+qn 为市场总产量、P为市场出清价格，且已知P=P(Q)=a-Q(当Q＜a时，否则P=0)。

博弈论与策略思维课后练习

博弈论与策略思维课后练习博弈论与策略思维课后练习判断题：1、理性的参与人应该选择劣策略。

[题号：Qhx008231]A、对B、错您的回答：B正确答案：B题目解析：理性的参与人应该选择占优策略，不应该选择劣策略。

2、石头剪刀布是序列博弈。

[题号：Qhx008227]A、对B、错您的回答：B正确答案：B题目解析：石头剪刀布是同步博弈。

3、三个火枪手游戏中甲提高生存策略的办法是放空枪。

[题号：Qhx008224]A、对B、错您的回答：A正确答案：A题目解析：甲通过改变策略，即放空枪有效提高了生存率。

4、海萨尼建立了“子博弈精炼纳什均衡”的概念。

[题号：Qhx008226]A、对B、错您的回答：B正确答案：B题目解析：海萨尼把不完全信息纳入到博弈论方法体系中；泽尔腾的贡献在于将博弈论由静态向动态的扩展，建立了“子博弈精练纳什均衡”的概念。

5、协调博弈只有一个纳什均衡。

[题号：Qhx008229]A、对B、错您的回答：B正确答案：B题目解析：协调博弈中至少有两个纳什均衡，具体是哪个均衡组合，需要博弈方协调。

单选题：1、“要想在现代社会做一个有文化的人，你必须对博弈论有一个大致了解”这是（）的名言。

[题号：Qhx008236]A、坎贝尔B、纳什C、萨缪尔森D、海萨尼您的回答：C正确答案：C题目解析：萨缪尔森的这句话意思为，你也许没必要深入学习博弈论高深的数学模型和推导，但它背后所包含的思维方法等是人类智慧的结晶，你应该要有所掌握。

2、情侣博弈是用（）来寻找纳什均衡的。

[题号：Qhx008244]A、占优策略法B、最优反应法C、逆向归纳法D、劣策略重复剔除法您的回答：B正确答案：B题目解析：占优策略法、最优反应法以及劣策略重复剔除法是寻找纳什均衡的三种方法，逆向归纳法主要用来推导有限重复博弈的结果。

3、在智猪博弈模型中，（）是纳什均衡。

博弈论战略分析入门第一章课后题答案

Instructor’s Guide to Game Theory: A Nontechnical Introduction to theAnalysis of StrategyChapter 1. Conflict, Strategy, and Games1.Objectives and ConceptsThe major objective of this chapter is to introduce the student to the idea that “serious” interactions can be usefully treated as games – what I have called the “scientific metaphor” at the root of game theory. Secondary objectives are to introduce the concepts of best-response strategies and the representation of games in normal form. Thus, the chapter starts with an example from war, which most people without preparation in game theory would think of as a most natural field for thinking of strategy, and the chapter begins with an example presented in extensive form, because it seems to be a more intuitive and natural way of thinking about strategy. Interweaved with this are some discussions of the origins of game theory. The chapter also takes up an episode from the movie version of “A Beautiful Mind,” since it seems very likely that many students will have seen the movie and it may be a major source of whatever ideas they have about game theory. The Prisoner’s Dilemma is the one example they are most likely to have seen in one or more other classes, so it belongs here, too.Using the Karplus Learning Cycle as a major organizing principle, I open with an example – the Spanish Rebellion – and only then introduce the general ideas it illustrates, and then follow with another example, NIM. Again, the discussion of the game in normal form begins with an example, the familiar Prisoner’s Dilemma, then proceeds to the general principles and follows with two more examples, the one from the movie and an advertising dilemma. This procedure is “psycho-logical” rather than logical, and someinstructors may not be familiar with it. However, I think it works well with most students, who can understand the general principles better if they have an example already in mind.Accordingly, the key concepts areDefinition of Game TheoryHistory and emergence of Game TheoryGame Theory as applicable to more than what we ordinarily think of as games.Representation in extensive form (tree diagrams)Best ResponseRepresentation in Normal Form2. Common Study ProblemsThe most important study problem probably will not actually emerge for a few class periods, but the roots are here in the first chapter: the concept of best response is difficult for some students, including some very good ones. Confusion may show up later in the form of a real difficulty in answering questions about social dilemmas: “How can this be a best response if it makes everybody worse off?” At this point, it may be helpful to emphasize that “best response” means the best response to other strategies that other players might choose, NOT necessarily a best response to the situation as a whole.Some (often very good) students may want to dispute whether the analysis of the Spanish Rebellion is really right. They have a point. It could be more completely represented as follows:Good Chance for Piust i s m Sure win for Pius But a) it doesn’t make any difference, since Hirtuleius will never choose to stay at Laminium, and give Pius a sure win. (That would not be subgame perfect, a concept we will get into in Chapter 14). b) Therefore, at the first step Hirtuleius commits himself to meeting Pius at the River Baetis, and it is that commitment that is shown by the firstdecision node. c) All game theory examples are simplified and abstracted in some ways,and we always need to take care that we have a simplification that focuses on theimportant points, rather than missing them. So it really is a good point to make, and this is a good example of the ways we need to be careful about our simplifying assumption.3. For Business StudentsThe major bait for business students in this chapter is purposely given a highprofile as the last example, the advertising game.4. Class AgendaFirst hour1) Get organizeda)Class Detailsb)Assignments2)Introductory presentation: What is Game Theory?Second hour1)Discussion of assignments, homework, etc.2)Discussion on Game Theory as a Scientific MetaphorDiscussion question: One issue in environmental policy is the passage ofresources on to the next and following generation. For example, forests andunderground aquifers can be of use to each generation, if they are preserved.However, if one generation uses them so intensively that they are destroyed,then future generations are deprived of that benefit. How might we capturethis as a “game?” Who are the players? What are the rules? Payoffs? Is theplay sequential or simultaneous?3)Play “The Environment Game” in class. Handout follows on the next page forconvenience in printing and copying.An In-Class GameFrom time to time in this class we will conduct some experiments with games, playing the games in class and discussing the results. Payoffs will be in GameBucks, and you will accumulate GameBucks throughout the class. Students’ GameBucks accumulations will be public knowledge. At the end of the class, students with above-average accumulations of GameBucks will get grade bonus points in proportion to the difference between the student’s accumulation and the class average. (Those below average will not be penalized). Your mastery of the principles of game theory should enable you to be more competitive in accumulating GameBucks.An Environment GameThis chapter focuses on the idea that “real-world” problems and interactions can be thought of as games. Environmental problems are often studied in game theoretic terms. One issue in environmental problems is the passage of resources on to the next and following generation. For example, forests and underground aquifers can be of use to each generation, if they are preserved. However, if one generation uses them so intensively that they are destroyed, then future generations are deprived of that benefit.For this game, students play in order, for example, around a circle from left to right. The first student is given a certificate with “One GameBuck” written at each end. The student has the choices of passing the certificate on to the next student in order, or tearing it in half and returning it to the instructor in return for two GameBucks. Each student who receives the certificate has the same choices, except the last. Each student who passes the certificate gets one GameBuck on his record. The last student can only pass it back to the experimenter for one point.The succession of students represents the succession of generations, each of which has the potential to get one GameBuck of benefit from the resource if it is preserved. The maximum benefit is equal to the number of students. If a student early in the ordering takes the opportunity to get two GameBucks, the total number of GameBucks awarded may be considerably less than this.5. Answers to Exercises and Discussion Questions1. The Spanish Rebellion. In her story about the Spanish Rebellion, McCullough writes "There was only one thing Hirtuleius could do: march down onto the easy terrain ... and stop Metellus Pius before he crossed the Baetis." Is McCullough right? Discuss.Yes, McCoullough is right. Hirtuleius must assume that Pius will respond to Hirtuleius’choice, and anticipate that response. If Hirtuleius marches for New Carthage, Pius will respond by taking Laminium and breaking out, the worst outcome for Hirtuleius. If Hirtuleius waits and marches for the River Baetis, Pius will march for New Carthage, with a good chance of beating Hirtuleius – Hirtuleius’ second worst outcome. But these are the only two possibilities, and second worst is better than very worse, so that is what Hirtuleius must choose.2. Nim. Consider a game of Nim with three rows of coins, with one coin in the top row, two in the second row, and either one, two or three in the third row. A) Does it make any difference how many coins are in the last row? B) In each case, who wins?a)Suppose there are just 2 pennies in the last line. Then Anna can take the one fromthe top line. Barbara is left with one of two choices – take 1 from either line,leaving the same game we had in the chapter, which we know Anna can win, ortake two from line, in which case Anna immediately takes the other two and wins.Thus first player wins in this case.b)Suppose there is just one in the last line. Then Anna can take the two from themiddle, leaving Barbara to take one of the others so Anna takes the remaining one and wins. Here again the first player wins.c)However, try what you will, you will find there is no way that Anna can win ifthere are three coins in the last row. Here, second player wins, so it does make adifference.There is a mathematical trick to figure out more complex games, fortunately, since a tree diagram for a Nim game with 3 coins in the last row would start out with 6 options for Anna and have from 3 to 5 for Barbara at the next stage, it would get pretty unwieldy. Do a Google search on “Nim” if you are interested in the trick.3. Matching Pennies. Matching pennies is a school-yard game. One player is identified as "even" and the other as "odd." The two players each show a penny, with either the head or the tail showing upward. If both show the same side of the coin, then "even" keeps both pennies. If the two show different sides of the coin, then "odd" keeps both pennies. Draw a payoff table to represent the game of matching pennies in normal form.OddHeads Tails EvenHeads2,00,2Tails0,22,0The standard of reading is assumed with the first payoff to even and the second to odd. (Even then odd.) 0- means wins no pennies; 2- means wins 2 pennies. Payoffs 1, -1 for wins one, loses one would be equally correct.4. Happy Hour. Jim's Gin Mill and Tom's Turkey Tavern compete for pretty much the same crowd. Each can offer free snacks during happy hour, or not. The profits are 30 to each tavern if neither offers snacks, but 20 to each if they both offer snacks, since the taverns have to pay for the snacks they offer. However, if one offers snacks and the other does not, the one who offers snacks gets most of the business and a profit of 50, while the other loses 20. Discuss this example using concepts from this chapter. How is the competition between the two tavern owners like a game? What are the strategies? Represent this game in normal form.Jim'sGive Snacks No SnacksGive Snacks20,2050,-20No Snacks-20, 5030,30TOM'SThis situation resembles a game because:• There is more than one player• Strategy is important• There are outcomes that depend on each player’s choice of strategyConsider the strategies and payoffs involved here. The basic strategies are: offerfree snacks, do not offer free snacks. If both offer snacks, their payoff is lower than if both do not offer snacks. However, if one bar chooses not to offer free snacks and the other does offer them, the potential payoff is superior to all other options.6. Quiz questionPlaced on the next page for convenience in copying and printing.Student name ____________________________Quiz – Game TheoryIn Game Theory at Work, James Miller writes: “When … my sister and I … were young teenagers, … Our mother told us she was going out into the yard but was expecting an important call. She told us to be sure to answer the phone when it rang.”(This was before home answering machines.) Neither teenager wanted to take the call, but each knew that unless one of them did so, they would both be punished for disobedience. What are the strategies? Represent this game in normal form.Answer:The strategies are “answer” or “don’t answer.” At this stage, this particular game needs to be expressed in normal form, since there is a “trick” to putting it into extensive form that will only be covered in the next chapter.SisterAnswer Don’tAnswer-2,-2-1,1JamesDon’t1,-1-5,-5Or, with qualitative rather than number payoffs,SisterAnswer Don’tAnswer Some confusion, someconfusionembarrassment, noembarrassmentJamesDon’t no embarrassment,embarrassmentpunished, punished1.11。

博弈论战略分析入门第二章课后题答案

Instructor’s Guide to Game Theory: A Nontechnical Introduction to theAnalysis of StrategyChapter 2. Games in Extensive and Normal Form1.Objectives and ConceptsThis chapter continues the discussion of the contrast between representation of games in extensive form and in normal form. A key concept here is that, as a matter of principle, any game can be represented in either form. The overall objective, then, is for the student to be able to take a game in one form and represent it in the other. But there are tricks to translating both ways, and these “tricks” are very important subsidiary objectives for this chapter:First, contingent strategies. For some games in extensive form, it is important that the strategies be expressed as contingent strategies. Failure to do this can lead to confusion, and this point is neglected in some texts. (I usually find it better not to offer horrible examples – since as certainly as I do, students give them back to me on quizzes, and explain that they were just doing what I said in class – and here it is right in their notes!) Contingency is itself an important concept, apart from its applications to Game Theory. It will be a new topic to many undergraduate students, and one that graduate students can use drill on. It leads on to a brief discussion of contingent planning. Applications of this concept are common in business but no less important in other fields related to decisions, such as military strategy, public policy, politics and law.Second, information sets. When decisions take place simultaneously, or one player is unaware of decisions already made by others, that player is in an informationset. In diagrams, this is represented by putting two or more branch points in the same oval. This is crucial in translating games like the Prisoner’s Dilemma into extensive form.Some of the games introduced in this chapter are important in themselves. In particular, the entry-retaliation game, in the first section, will recur in various forms again and again. Thus, clear understanding of this game should be another objective of the class.Accordingly, the key concepts areExtensive and normal form as alternative representations for any game.Contingent strategiesContingency planningInformation setsEntry and retaliation gamesCredibility of threatsmon Study ProblemsThe devil is in the details. It is pretty easy to memorize the definitions of contingent strategies but more difficult to apply them. It is probably enough, for this course, if the students are aware of the need for contingent strategies and don’t let it slip by – but (speaking for myself) I have to puzzle a lot over how to make the contingencies complete enough. Even in texts that do not neglect this concept, its application in practice is complicated and even simple examples can be demanding. (It belongs this close to the beginning of the book only because it is so basic for so many things that follow).Something similar seems to apply to information sets. Here, students seem usually to be able to recognize them when they see them (not without a certain number of false starts) but rarely take the initiative to use them when presented with new problems. Again, that level of mastery is generally sufficient for the course.Drawing both tables for normal form games and diagrams for games in extensive form can be challenging, but extensive form games are especially tricky for students who don’t happen to be up on drafting software. One of my students found an ingenious way to draw the diagrams in an Excel spreadsheet. It is shown in the answers to question 2.3.For Business StudentsHere, again, the business draw is pretty obvious, and leads off the chapter with a living–with-deregulation example.4.Class AgendaIn my undergraduate class, I show “A Beautiful Mind” the second week. This substitutes for one or more class hours – special arrangements are necessary as the movie runs nearly four hours. Discussion question: Does the Movie Nash give good advice in the bar? Answer – looks like not, since his proposals don’t correspond to a best response.However, these agendas do not assume that the movie has been shown.First hour:1)Quiz on earlier material2)Introductory presentation: Games in Normal and Extended Form•Assignments3)Discussion question: how can we make contingency plan for the emergence ofnew epidemics like SARS (which emerged in the spring of 2003)?Second Hour:1.Discussion of quiz and assignments2.Play a retaliation game in class. Handout follows:A Two-Part GameHere is a two-person game that is played in two stages. Each student will play each role. It works like this: player 1 chooses between two strategies: “aggressive” and “not aggressive.” If player 1 chooses “not aggressive,” then each player receives 3 GameBucks. If player 2 chooses “aggressive,” then player 2 must choose between “retaliate” and “accommodate.” If player 2 chooses “accommodate” then player 1 gets 5 GameBucks and player 2 gets 1 GameBuck. If player 2 chooses “retaliate,” then no-one gets any GameBucks.As player 1, you should fill in your name and your strategy choice below. The sheets will then be taken up and redistributed at random. You will receive a new sheet on which someone has already filled in the first stage choices. Fill in your name and your strategy choice or NA if your player 1 has chosen “not aggressive.”Player 1Student name ____________________________My strategy is (circle one)AggressiveNot aggressivePlayer 2Student name ____________________________My strategy is (circle one)RetaliateAccommodateNA3.Discussion: How could we represent this game in extended form? How aboutnormal form?Answers in handout on next page.Analysis of the Two-Part Agression-Retaliation Game120,05,13,3Player 2If player 1 is aggressive thenretaliate; if player 1 is not,then do nothing.If player 1 is aggressive thenaccommodate; if player 1 is not,then do nothing.aggressive0,05,1 Player1not3,33,35. Answers to Exercises and Discussion Questions1. Sibling Rivalry. Two sisters, Iris and Julia, are students at Nearby College, where all the classes are graded on the curve. Since they are the two best students and their class, each of the will top the curve unless they enroll in the same class. Iris and Julia each have to choose one more class this term, and each of them can choose between math and literature. They're both very good at math, but Iris is better at literature. Each wants to maximize her grade point average. The grade point averages are shown in the table below, which treats their friendly rivalry as a game in normal form.()Table E. 1. Grade Point Averages for Iris and JuliaIrismath litmath 3.7,3.8 4.0,4.0Julialit 3.8,4.0 3.7,4.0What are the strategies for this game? Express this game in extended form, assuming that the sisters make their decisions at the same time. Express this game in extended form, assuming that Iris makes her decision first, and Julia knows Iris's decision when she chooses her strategy.Suppose Iris doesn’t care what her own grade point average is, but she wants to maximize the difference between her grade point average and her sister's – just to show the little twerp up! (But Julia still wants to maximize her grade point average and is notconcerned about how her sister does.) Write the table for the game in normal form under this assumption, and redo the last three questions. What strategy will Iris choose if she chooses first?The strategies for Julia are to take Math or Lit, and the strategies for Iris are to take Math or Lit. Each sister will base her strategy on maximizing the absolute value of her GPA.Assuming the sisters make their decisions simultaneously, the extended form representation of the game is below:What will happen? Iris can assure herself of a 4.0 by choosing Lit, so probably that is what she will do. Anticipating that, Julia can get her 4.0 by choosing Math.This is the game in extended form assuming that Iris chooses first and Julia knows Iris’ DecisionWhat happens? Iris can now choose either strategy and be sure of her 4.0. If Iris chooses Math, Julia will choose Lit for 3.8 rather than 3.7. So we can no longer be sure that Iris will choose Lit.The New Game in Normal form is as followsIris MathLit Math3.7 , 0.14.0 , 0.0JuliaLit 3.8 , 0.2 3.7, 0.3Here is the game in extended form with simultaneous decisions:It is now pretty difficult to guess what will happen, since Iris will get the greater difference by competing directly with her sister and enrolling in whichever class her sister does, but Julia wants to do just the opposite – enroll in whatever class her sister does not. We will need some advanced analysis to figure out what will happen here!Here is the new game in extended form if Iris goes first:In this case we can do a little better. If Iris chooses Math then Julia will choose Lit – giving Iris a margin of 0.2. However, if Iris chooses Lit then Julia will choose Math, leaving Iris with 0.0. Therefore, Iris will choose Math and Julia will choose Lit.One thing we see from this example is that “little things mean a lot.” If some players are motivated by relative rather than absolute payoffs, it can make a difference; and if one player goes first rather than having both choose simultaneously, that, too, can make a difference.2. The Great Escape. A prisoner is trying to escape from jail. He can attempt to climb over the walls or dig a tunnel from the floor of his cell. The warden can prevent him from climbing by posting guards on the wall, and he can prevent the con from tunneling by staging regular inspections of the cells, but he has only enough guards to do one or the other, not both.What are the strategies and payoffs for this game? Express the payoffs in both non-numerical and numerical terms. Express this game in normal form. Express this game in extended form, assuming that the prisoner and the warden make their decisions at the same time. Express this game in extended form, assuming that the warden makes his decision first, and the prisoner knows the warden's decision when he chooses his strategy.There are two payoffs in the game depending on the player. For the prisoner, his payoff is freedom, or not getting caught by the guards while trying to escape. For the warden, his payoff is preventing the escape of the prisoner. The number “10” denotessuccess for the party, and “0” represents failure for the guards and a “-10” represents 10 more years in prison for the prisoner.If the prisoner were to attempt to climb the wall and the guards just happened to be protecting the wall, then the guards would be successful, receiving a “10” for their job well done and the prisoner receives 10 more years in jail for being caught trying to escape. However, if the prisoner were to dig a tunnel while the guards were protecting the wall, then the prisoner receives a “10” for success, or his freedom. The guards would receive a “0” for failing at their job.The strategies for the prisoner are dig or climb, while the strategies for the warden are to guard the walls or inspect the cells.Normal form:WardenProtect Wall Inspect Jail CellsClimb Wall-10,1010,0PrisonerDig Tunnel10,0-10,10Extended Form, Simultaneous decision:wall10,-10walltunnel0,10prisonerWardenwall0,10inspecttunnel10,-10Extended Form, Warden decides first:Wall10,-10wall prisonerTunnel0,10WardenWall0,10inspect prisonerTunnel10,-10Black WinsSince every move black can make leads to a move that can give red a win, red will win this game if both play their best strategies.4. It's good to be da Queen? Queen Elizabeth the First of England faced a difficult strategic problem. On the one hand, if she married, she would no longer have power since, under the customs of the time, her husband would assume all the power of a king. Elizabeth had seen how her father Henry treated several of his queens, with imprisonment or execution. On the other hand, if her nobles had known she would never marry and leave an heir to the throne, they would have seen rebellion as a lesser evil. That's why Liz kept her boyfriend Dudley on the string so long.Treat this problem as a game in which the players are Elizabeth and her nobles. What are their strategies? Express the game in both extensive and normal form. Are there any information sets?Queen Elizabeth’s objective is to retain her regal powers, while her nobles are interested in succeeding to the throne in the absence of what they considered a credible head of state. For the purposes of this game, a credible head of state is one that has regal powers and the potential to pass that credibility to an heir. Liz’s strategies are to marry or not marry and the nobles’ strategies are to rebel or not rebel.Payoffs are based on the following rationale: If Liz marries and the nobles rebel, their actions are completely unjustified and they lose their noble status in society. If she marries and they do not rebel, then everything happens as the world expects, causing no net change in the nobles’ status. However, by marrying, Liz loses her regal autonomy. Alternatively she might decide not to marry. If the nobles do not rebel, Liz keeps her autonomy and they keep their rank. If they do rebel, Liz loses her autonomy and the nobles all shift one position up the feudal ladder.The game is represented in both normal and extensive form below. An information set exists for Liz’s strategies because the nobles must decide to rebel or not without knowing whether Liz will ever marry or not.5. Nim strikes again. Translate the game of Nim (Chapter 1) from extensive to normal form.Nim in Normal FormAnnaTake one coin from top row Take onecoin from thesecond rowTake bothcoins fromsecond rowIf Anna takes one fromtop row, take one; ifAnna takes one from thesecond row, take onefrom the first row; ifAnna takes both coinsfrom the second row,take the remaining coinAnna wins Anna wins Barbara winsIf Anna takes one fromtop row, take one; ifAnna takes one from thesecond row, take onefrom the second row; ifAnna takes both coinsfrom the second row,take the remaining coinAnna wins Anna wins Barbara winsIf Anna takes one fromtop row, take two; ifAnna takes one from thesecond row, take one from the first row; if Anna takes both coins from the second row, take the remaining coin BarbarawinsAnna wins Barbara winsBarbaraIf Anna takes one fromtop row, take two; ifAnna takes one from thesecond row, take one from the second row; if Anna takes both coins from the second row, take the remaining coin BarbarawinsAnna wins Barbara winsNim in Normal Form with Numeric OutcomesAnnaTake one coin from toprowTake onecoin from thesecond rowTake bothcoins fromsecond rowIf Anna takes one from toprow, take one; if Anna takesone from the second row,take one from the first row;if Anna takes both coinsfrom the second row, takethe remaining coin-1,1-1,11,-1If Anna takes one from toprow, take one; if Anna takesone from the second row,take one from the secondrow; if Anna takes bothcoins from the second row,take the remaining coin-1,1-1,11,-1If Anna takes one from toprow, take two; if Anna takesone from the second row,take one from the first row; if Anna takes both coins from the second row, take the remaining coin 1,-1-1,11,-1BarbaraIf Anna takes one from toprow, take two; if Anna takesone from the second row,take one from the secondrow; if Anna takes bothcoins from the second row,take the remaining coin1,-1-1,11,-16. Quiz questionPlaced on the next page for convenience in copying and printing.Student name ____________________________Quiz – Game TheoryHere is a "tree diagram" of a game in extended form. The players are Joe (player J) and Irving (player I). Joe's strategies are "up " and "down," and Irving's strategies are "left" and "right."1)Write the payoff table to represent this game "in normal form."2)Explain what it means that Joe's decision's are shown in a single oval areaAnswer:Jleft rightup3,35,2Idown2,51,1The elongated oval is an information set, and it means that Joe does not know Irving’s decision when Joe makes his decision.2.21。

博弈论各章节课后习题答案 (4)

第四章谈判与协调1.帕累托占优均衡和纳什均衡的关系是什么?纳什均衡的基本思想是：每一个局中人选择一个策略，由所有局中人的策略构成了一个策略组合；在其它局中人选定策略不变的情况下，若某一个局中人单独地违背自己已选的策略，那么他的收益只会下降（或收益不会增加）。

这样的策略组合构成一个均衡局势，并命名为纳什均衡。

纳什均衡有纯策略的纳什均衡和混合策略的纳什均衡。

一个博弈中有不止一个纳什均衡时，就构成一个多重纳什均衡问题。

在多重纳什均衡下给出一些选择标准就得到一些特定的纳什均衡。

其中帕累托占有纳什均衡是根据这样的选择标准选择的均衡。

在博弈中，若均为G 的其纳什均衡，若满足[,{},{}]i i G N S P =12,,,m s s s ∗∗∗⋯0i s ∗，0()()i i i j P s P s ∗∗>1,2,,,1,2,,i n j m==⋯⋯则称为博弈G 的帕累托占优纳什均衡。

可见帕累托占有纳什均衡是纳什均衡中收益最大0i s ∗的一种均衡。

2.分别找出具有下列性质的2人博弈的例子。

(1)不存在纯策略纳什均衡；(2)至少有两个纳什均衡，并且其中之一是帕累托占优均衡。

（1）不存在纯策略的纳什均衡：该博弈不存在纯策略的纳什均衡（2）该博弈有三个纳什均衡：（战争，战争）、（和平，和平）和一个混合策略纳什均衡。

很显然，（和平，和平）是一个帕累托占优纳什均衡。

2525((,),(,77773.假设在某一产品市场上有两个寡头垄断企业，它们的成本函数分别为：TC 1=0.1q +20q 1+100000TC 2=0.4q +32q 2+200002122这两个企业生产一同质产品，其市场需求函数为：Q=4000-10p 。

试分别基于古诺模型和纳什谈判模型求解两企业的利润。

解：由和400010Q p =−12Q q q =+得124000.1()p q q =−+战争和平国家1战争-5，-58，-10和平-10，810，10所以：[]21121114000.1()(0.120100000)q q q q q π=−+−++211213800.10.2100000q q q q =−−−[]22122224000.1()(0.43220000)q q q q q π=−+−++221223680.10.520000q q q q =−−−12113800.10.40q q q π∂=−−=∂21223680.10q q q π∂=−−=∂21123800.10.403680.10q q q q −−=⎧⎨−−=⎩求解方程组得12880280q q =⎧⎨=⎩将，代入到，中去得到最优解1q 2q 1π2π*1*25488019200ππ⎧=⎪⎨=⎪⎩4.你能否对如下的CG-2×2博弈中x 的变化设计出一些实验方案，来讨论是帕累托占优思想还是风险占优思想在策略选择中起主要作用。

博弈论课后题答案

博弈论课后题答案(总9页)--本页仅作为文档封面，使用时请直接删除即可----内页可以根据需求调整合适字体及大小--;第二章第三章PPT问题第四章第五章第六章一、用柠檬原理和逆向选择的思想解释老年人投保困难的原因。

答：“柠檬原理”是在信息不完美且消费者缺乏识别能力的市场中，劣质品赶走优质品，最后搞垮整个市场的机制。

“逆向选择”是在同样不完美信息和消费者缺乏识别能力的市场中，当价格可变时，价格和商品质量循环下降，市场不断向低端发展的机制.高龄人群的保险市场是一个典型的柠檬原理和逆向选择会起作用，从而会导致发展困难的市场。

老年人的健康情况差别很大，比年轻人之间的差别要大得多，而保险公司要了解老年人投保人的实际健康状况又很困难或成本很高，这就造成了保险公司对老年投保人健康状况的信息不完美。

则保险公司就无法根据每个老年投保人的实际健康情况确定不同的保费率，只能根据平均健康情况确定保费率。

这种平均保费率对健康情况很差的老年人是合算的，但对健康状况较好的老年人则不合算。

因此前者倾向于投保，后者则不愿意投保，这就会导致投保的老年人的平均健康情况会很差。

这使得保险公司的赔付风险大大提高，不仅不能赢利而且要亏损，从而失去经营老年保险的积极性，最终导致老年人的投保难问题。

这就是柠檬原理作用的结果。

如果允许调整保费率，那么保险公司为了避免亏损会上调保费率。

而这又会使得原来投保或者准备投保者中相对较健康的老人退出，从而投保老人的平均健康状况会变得更差。

如此循环，最终保费会升得很高而投保老人的平均健康情况则会越来越差，对市场的发展当然是很不利。

这就是逆向选择作用的结果。

二、为什么消费者偏好去大商店买东西而不太信赖走街穿巷的小商贩消费者去大商店更接近无限次重复博弈，商场提供高质量产品的概率更大，虽然个别消费者不一定能对商店以往售出商品的质量作出反应，但消费者群体肯定可以作出反应，因此大商店保持高质量符合自己的长期利益，一股会自觉保证质量，从而消费者也比较可以信任大商店的商品。

博弈论书后习题

第一章1．下图是两人博弈的标准式表述形式，其中参与者1的战略空间},{1D U S =，参与者2的战略空间},{2R L S =。

参与者2 参与者1LR D U这里h g f e d c b a ,,,,,,,为参数。

（1）设),(*L U S =是此博弈的占优战略均衡，问：上述参数之间应满足哪些条件？（2）设),(*R U S =是此博弈的逐步剔除严格劣战略均衡，问：上述参数之间应满足哪些条件？（用两种剔除顺序讨论）（3）设),(*R D S =是此博弈的纳什均衡，问：上述参数之间应满足哪些条件？（4）设),(*1L U S =和),(*2R D S =是此博弈的纳什均衡，问：上述参数之间应满足什么条件？这时两个参与者有无严格劣战略？2．在下图所示的标准式表述的博弈中，找出逐步剔除严格劣战略均衡。

参与者2 参与者1 LM MUD R 3.在下图所示的标准式表述的博弈中，哪些战略不会被重复剔除严格劣战略所剔除？纯战略纳什均衡又是什么？参与者2 参与者1 LC MTB R 4.下图所示的标准式表述的三人博弈中，参与者1的战略空间},{1D U S =，参与者2的战略空间},{2R L S =，参与者3的战略空间},,{3C B A S=。

参与者1选择两行中的某一行，参与者2选择两列中的某一列，参与者3选择三个矩阵的某矩阵。

找出此博弈的纯战略纳什均衡。

LR D UA L RB L R C5.(投票博弈)设有三个参与者)3,2,1(=i 要在三个项目（A,B 和C ）中投票选出一个。

三个参与者同时投票，不允许弃权。

因此，三个参与者的战略空间为)3,2,1}(,,{==i C B A S i 。

得票最多的项目被选中。

如果没有任何项目得到多票数，那么项目A 就被选中。

某个项目被选中后三个参与者的收益函数如下：2)()()(321===C u B u A u1)()()(321===A u C u A u0)()()(321===B u A u C u（1）写出此博弈的标准式表达；（2）求出此博弈的纯战略纳什均衡。

博弈论各章节课后习题答案

9. 求如图所示完全信息动态博弈的子博弈完美纳什均衡（图中数字(a,b,c)分别表示局中人 1、
2、3 的收益）。
1
A1
A2
3
2
C1
C2
B1
B2
(4,2,3)
(1,7,8) 3
C1
C2 C1
3
C2
(5,4,3) (7,6,6) (2,1,9) (0,4,2)
答：局中人 1 采取 A2 行动，局中人 2 采取行动 B1 时，局中人 3 必然采取 C2 行动（因为 3<6），因而该博弈的顶点只能是(7,6,6)。同样对于局中人 3 右边一个子博弈，必然采取 C1 行动（9>2），因而该博弈的顶点只能是(2,1,9)。进而原博弈简化为：
的定价,qi是企业i的需求量。假设企业生产没有固定成本,并且边际成本为常数c,c<a.假定博弃重复无穷多次,每次的价格都立即被观察到,企业使用触发策略。求使垄断价格可以作为完美均衡结果出现的最低贴现因子δ,并解释δ与n的关系。
分以下几个步骤进行。
1)计算纳什均衡当企业 i 选择价格 pi,其它企业选择价格 pj(j=1,2,…,n,j≠i)时,企业 i 的利润为: πi = (pi − c)qi = (pi − c)(a − pi + b(p1 + p2 + ⋯ + pi−1 + pi+1 + ⋯ + pn )) ,i=1,2,…,n
∂π2 ∂q 2
= a − q1
− 2q2
− q3
−c=0
∂π3 ∂q3
=
a
− q1
− q2
− 2q3
−c

博弈论与策略思维课后练习

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