2013经济博弈论期中答案

名字班学号1经济游戏理论经济游戏理论经济游戏理论(2013年春季学期春季学期春季学期春季学期)game theory midtermanswers(spring 2013)期中考试，期中考试，期中考试，期中考试，期中考试正确答案(2013/请列出所有问题的答案。请把所有问题的答案写在答题纸上。请把所有问题的答案写在答题纸上，把所有问题的答案写在答题纸上。请不要在这张试卷上写。这个测试面总是无效的。对这个测试面总是无效的。对这个测试面总是无效的。即可从workspace页面中移除物件。即可从workspace页面中移除物件。即可从workspace页面中移除物件。note : please write all you answers on the answer book . problem 1。(14 pts) true or false？explain . give examples to illustrate your answers if needed。(1)if a player has a dominant strategy in a simultaneous-move game，Then she is sure to get her best possible outcome。false。a dominant strategy yields you the highest pay off available to you against east each of your oppo Nent s strategies。playing a dominant strategy does not guarantee that you end up with the highest of all possible payoffs。in the prisoners dilemma Ame，both players have dominant strategies，But neither gets the highest possible payoff in the equlibrium out(2)when A two-by-two game has A mixed-strategy equlibrium，A player s equlibrium mixture is designed to yielher the same expected payThus，A player s equlibrium mixture yields the opponent the same expected pay off against each of the player s pure strategies .but it would not necearily Yield the player himself the same expected payoff against the opponent s pure strategies .an example would be a chicken game，Where the equiprium mixture(1/2s w1/2 ST)of a player will give her payoff of 1/2 * 0the pay off is unequal.note，however，That the statement will be true for zero-sum games，because when your opponent is indfferent in sun问题2 .莫妮卡和南希合伙提供高尔夫行业的咨询服务.他们每个人都必须决定对这项工作作出多大的努力。摩妮卡在事业中的努力程度为m，n表示南希努力的程度。该同业项目的共同利益为4m 4n Mn .万美元。两个伙伴平分了这些利益。可是，这是莫妮卡的m2，南希的N2，每一个人努力的成本，一万美元。每个合作伙伴必须在不知道其他参与人工作有多努力的情况下，决定其努力程度。Problem 2 .(20 pts)Monica And Nancy have formed a business partnership to provide consulting services in the golf industry . they each have to decide how mowthe joint profits of the partnership are given by 4m 4n Mn，in tens of thousands of dollars，And the two partners split these profits equally . huallyThe cost to Monica of her effort is m2，While the cost to Nancy of her effort is N2(both measureed in tens of thousands of dollars)。each partner must make effort decision名称类别2 without knowing what effort decision the other player has made。(a)这个博弈的纳什均衡是什么？(8分)what is the Nash equlibrium to this game？(8 pts)Monica maximizes her net profits by choosing M，Given N . her problem is : max M(1/2)(4m 4n Mn)-m2 thus(净利润减去努力的成本)(4分)instead of maximizing their own net profit，if the two players want to maximize their joint net profits，how much(net profits are defined as profits MINUS costs from making eforts。)(4 pts) the problem is : max m，n (4m 4n Mn)-m2-N2。the solution is : mo=no=4。现在，假设莫妮卡和南希按顺序选择，而不是同时选择努力程度。摩妮卡承诺先选择这一努力，南熙观察到这一选择后，选择自己的努力。assume now that Monica and Nancy choose their effort levels sequencalelly instead of simultaneous。Monica commits to her choice of effort first，And on observing this decision，Nancy commits to her own effort。(c)这个博弈的子博弈完美均衡是什么？(6分)what is the subgame-perfect equlibrium to the game？(6 pts) By backward induction，Nancy chooses her best response to Monica s choice . Nancy s choice is exactly her best response curvegiven Nancys best response curve，Monica chooses her effort to maximize her own net profit as 3360 max m(1/2)(4m 4n Mn)the SPE is that Monica chooses effort of 12/7，And Nancy chooses effort of 1 (1/4) m，where m is Monicas effort。in equlibrium Nancy chooses effort of 10/7。(d)这个游戏有先驱或后辈的优点吗？说明。(两点)does this game have a first-Mover or a second-Mover advantage？Explain。(2 pts)the net profit each partner earns in the simultaneous-move game(part(a)can be calculated as 40/9；the net profit each partner earns here in the sequential-move game is 224/49 for Monica and 268/49。each partner s profit in sequential-move game is larger than in simultaneous-move game，But the second-Mover s profit is ever现在，莫妮卡和南希决定谁先努力(或不先努力)。为此，一个人又在一张纸条上写下了她是否答应做善事。如果两个人都写了“是”或“否”，他们同时选择了努力的程度。如果莫妮卡写了“是”，南希写了“否”，莫妮卡答应做善事。反之亦然。now Monica and Nancy need to decide which(if either)of them will commit to an effort level first .to do this，Each of them simultaneous ly writes on a separate slip of paper whether or not she will commit first。if They both write yes or They both write no ，They choose effort levels simultaneous ly。if Monica writes“yes”and Nancy writes“no”，“then Monica commits to her move first .if Monica writes“no”and