经济博弈论（2007年秋季学期）
期中测验题答案
(2007/11/15)
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）。
1、找出下列博弈要求的全部均衡（要求见各小题）。指出均衡结果．．
及每个参与者完整的均衡策略．．
。（20分） Find all the required equilbria (specified in each part) for the following games. Identify the equilibrium outcome and the complete equilibrium strategy for each player. (20 points)
（1）反转均衡（或子博弈完美均衡）（6分）
Rollback equilibria (or subgame perfect equilibria, SPEs) (6 points)
A’s equilibrium strategy is (N1, N4, N5), or “Always N.” B’s equilibrium strategy is “b if N” (or just “b”). C’s equilibrium strategy is “d if S” (or just “d”). Equilibrium payoffs are (2, 3, 2).
(A, B, C)
（2）纯策略纳什均衡（6分）
Pure-strategy Nash equilibria (6 points)
COLUMN
East
Center
West
North 2, 3 8, 2 10, 6
ROW
Up 3, 0 4, 5 6, 4
Down 5, 4 6, 1 2, 5
South 4, 5 2, 3 5, 2
NE: (North, East). Payoffs: (10, 6) (shown in the figure)
（3）纯策略及混合策略纳什均衡（8分）
Pure- and mixed-strategy Nash equilibria (8 points)
COLUMN
A B C D ROW
1 1, 1 2,
2 3, 4 9, 3
2 2, 5 3,
3 1, 2 7, 1
Pure-strategy NE: (1, C) and (2, A). Payoffs: (3, 4) and (2, 5) (shown in the figure) (2 points each) Mixed-strategy NE: For Player Column, strategy D is dominated by C; strategy B is dominated by
a 50-50 mixture of A and C. So you need consider a 2*2 game only. Using the opponent indifference, the unique mixed-strategy equilibrium is ((1/2)*1, (1/2)*2) and ((2/3)*A, (1/3)*C). Payoffs are (5/3, 3). (4 points)
2、进入与阻止进入（20分）Entry and Deterrence (20 points)
考虑空客和波音之间在开发新的商用喷气式飞机上的竞争。假定波音在开发过程中已经
捷足先登，空客还在考虑是否要进入与之竞争。如果空客不进入，它获得零利润，而波音得
到垄断利润10亿美元；如果空客决定进入并开发竞争产品，那么波音就不得不决定是与空
客和平相处还是发起价格战。在和平相处的情况下，每个企业获得3亿美元的利润。如果价
格战打响，飞机的价格会暴跌，每个企业都入不敷出，会亏损1亿美元。
Consider the rivalry between Airbus and Boeing to develop a new commercial jet aircraft. Suppose Boeing is ahead in the development process and Airbus is considering whether to enter
the competition. If Airbus stays out, it earns zero profit, whereas Boeing enjoys a monopoly and earns a profit of $1 billion. If Airbus decides to enter and develop the rival airplane, then Boeing
has to decide whether to accommodate Airbus peaceably or to wage a price war. In the event of peaceful competition, each firm will make a profit of $300 million. If there is a price war, each
will lose $100 million because the prices of airplanes will fall so low that neither firm will be able
to recoup its development costs.
(a)画出博弈树。找到反转均衡并描述每个企业的均衡策略。（10分）
Draw the tree for this game. Find the rollback equilibrium and describe the firms’ equilibrium strategies. (8 points)
Tree shown as below. Rollback shows that Boeing chooses peace over war if Airbus enters, so Airbus will enter. Rollback equilibrium entails Airbus playing “enter” and Boeing playing “peace
