经济博弈论期末测验答案_2007

When career choices are made in an uncoordinated way, what are the stable equilibrium outcomes?
(6 points) 如图。有两个稳定均衡结果：N*=0，N*=90（或 89）。 （当有 0 个律师时，没有人愿意从工程师转为律师，因为 1 个律师的收入为 100*1-12-800=-699<100（工程师收入）。 当有 90 个律师时，律师收入 100*90-902-800=100，刚好等于工程师收入。此事律师转成工 程师无所谓。但工程师不愿意转为律师——此时律师人数为 101，收入小于 100。 当有 89 个律师时，律师收入大于 100，不愿意转为工程师。工程师如果转为律师，律师变 成 100 人，收入 100——等于工程师，因此工程师无所谓。） （c）假定整个班一起来决定多少人应该去当律师，以最大化整个班总的纯收入。将会有多 少个律师？（6 分）
and Right for Column. (This is a prisoners’ dilemma.)
Commitment cannot be used.
Row can improve his payoff from 2 to 3 by using promise “Down if Left”. The implied threat is
Up Row
(0, 0) (Row, Column)
Left
Down
(2, 1)
Column
Right
Up Row
Down
(1, 2) (0, 0)
(b)（6 分）
COLUMN
Left
Right
ROW
Up
4, 3
3, 4
Down
2, 1
1, 2
The NE is (Up, Right) with payoffs (3, 4). Both players have a dominate strategy – Up for Row
3
姓名
班级
Column
Up Row
Left
Down
Right
Up Row
Down
学号
(4, 3) (Row, Column) (2, 1) (3, 4) (1, 2)
(c) （6 分）
COLUMN
Left
Right
ROW
Up
4, 1
2, 2
Down
3, 3
1, 4
The NE is (Up, Right) with payoffs (2, 2). Both players have a dominate strategy – Up for Row
姓名
班级
学号
经济博弈论（2007 年秋季学期） 期末测验题答案 (2008/1/3)
注意：请将所有题目的答案写在答题册上，写在本试题页上一律无效（需要的图表请重画）。
一、职业选择的集体行动博弈 Collective-action Games of Career Choice（15 分） 假定一个班有 100 个学生，他们正在比较两种职业选择——律师或工程师。一个工程师
secretary, paralegals, access to online reference services, and so forth) is $800,000. So each lawyer takes home 100N-N2-800 thousand dollars a year when there are N of them. （a）画一个图。用纵轴表示每个律师的纯收入，横轴表示律师人数。（3 分）
and Right for Column.
Commitment cannot be used.
Row can improve his payoff from 3 to 4 by using threat “Down if Right”. The implied promise is
“Up if Left”. The game tree is as below. Payoffs are (4, 3) for Row and Column.
1
姓名
班级
学号
班收入的律师人数为 62 人。（3 分）
Lawyer
100
NE1
-800
0
10
Engineer N
NE2 100
-800 89 或 90 100
二、策略性行动 Strategic Moves（20 分） 对于以下的三个博弈，回答下列问题：（1）如果没有参与者使用策略性行动，纯策略纳
什均衡是什么？（2）参与者 ROW 能否通过某种策略性行动，如承诺，威胁或许诺，或它 们的某种组合，使得自己收益提高？找出所．有．可能的策略性行动，并用带有策略性行动的博 弈树来演示你的答案。
play are shown as the table below, where a larger number of years mean a lower payoff:
moves. (a) （8 分）
COLUMN
Left
Right
ROW
Up
0, 0
2, 1
Down
1, 2
0, 0
The NEs are two: (Up, Right) and (Down, Left). (This is a battle of sex.)
Row can improve his payoff, i.e., fix one of the NEs he prefers, by using commitment, i.e., moving
who choose this career. Lawyers make work for one another; so, as the total number of lawyers
increases, the income of each lawyer increases – up to a point. Ultimately, the competition
first. The game tree is as below. The SPE is (Up; Right if Up and Left if Down) with payoffs (2, 1)
for Row and Column.
2
姓名
班级
学号
Left Column
(0, 0)
(Row, Column)
payoff by using a strategic move, i.e., commitment, threat, promise, or a combination of such
moves? Find out all the possibilities and show your answers by using game trees with strategic
outcome combination, Column only gets her worst payoff 1.)
Up Row
(4, 1) (Row, Column)
Left
Down
(3, 3)
Column
Right
Up Row
Down
(2, 2) (1, 4)
三、囚徒困境的进化博弈 Evolutionary Game of Prisoner's dilemma（20 分） 考虑一个有两种表现型的种群：天生的合作者（不承认）和天生的背叛者（承认）。当
Now suppose the whole class decides how many should become lawyers, aiming to maximize the
total take-home income of the whole class. What will be the number of lawyers? (6 points) 全班总收入表示为： T(N) = N*(100N-N2-800)+(100-N)*100= 10,000-900N+100N2-N3. 该总收入最大化的一阶条件为： T’(N) = -900+200N-3N2=0 ⇒ N≈62, or N≈5. 可以验证，当 N=62 时总收入最大（另一个解 N=5 得到总收入的一个极小值）。即最大化本
Suppose a class of 100 students is comparing the choice between two careers – lawyers or
engineers. An engineer gets a take-home pay of $100,000 per year, irrespective of the numbers
Draw a graph showing the take-home income of each lawyer on the vertical axis and the number
of lawyers on the horizontal axis. (3 points) 见下图。 （b）当职业的选择以一种未经协调的方式来进行，稳定的均衡结果有哪些？（6 分）
For each of the following three games, answer these questions: (i) What is the pure-strategy Nash
equilibrium if neither player can use any strategic moves? (ii) Can one player, ROW, improve his