EC 399 Final Exam
电子商务 Suppose Larry first win $3000 in a casino two days ago. Then he lost another $300 in the stock mar- ket x < 0. Assume that Larry’s ···
Problem 1 (20 pts)
Suppose Larry first win $3000 in a casino two days ago. Then he lost another $300 in the stock mar- ket x < 0. Assume that Larry’s value function is given by v(x) = x/3 when x ≥ 0; v(x) = −3√−x when x < 0.
- What is the total value of Larry if he integrates the gain and the loss? What is the total value of Larry if he separates the the loss from gain? From Larry’s view, should he integrate or separate? (10pts)
- Please draw the graph that illustrates the values corresponding to Larry’s gain and loss and the integration of the (10pts)
Problem 2 (30pts)
Assume that JB is going to watch one movie. He can go to Movie A in week 1, or go to Movie B in week 2, or go to Movie C in week 3. Suppose Movie A gives him a utility of 3, Movie B gives him a utility of 5, Movie C gives him a utility of 8.
- Suppose that JB is an exponential discounter with parameter δ = 0. Which movie wouldhe eventually watch? Try to depict the three movies on a graph and draw the different time indif- ference curves that go through them. (10 pts)
- Suppose that JB is a naive hyperbolic discounter with parameter δ = 0.9 and β = 0. Which movie would he eventually watch? (10pts)
- Suppose that JB is a sophisticated hyperbolic discounter with parameter δ = 0.9 and β = 0. Which movie would he eventually watch? (10pts)
译文：问题 1（20 分） 电子商务
假设拉里两天前第一次在赌场赢了 3000 美元。然后他在股票市场上又损失了 300 美元 x < 0。假设当 x ≥ 0 时，拉里的价值函数由 v(x) = x/3 给出； v(x) = −3√−x 当 x < 0 时。
如果 Larry 整合收益和损失，他的总价值是多少？如果将损失与收益分开，拉里的总价值是多少？在拉里看来，他应该整合还是分离？ (10 分)
请绘制图表，说明与拉里的得失对应的值以及（10 分）的积分
问题2（30分）
假设 JB 将看一部电影。他可以在第 1 周去看电影 A，或者在第 2 周去看电影 B，或者在第 3 周去看电影 C。假设电影 A 给他的效用是 3，电影 B 给他的效用是 5，电影 C 给他他的效用是 8。
假设 JB 是参数 δ = 0 的指数折扣器。他最终会看哪部电影？尝试在图表上描绘这三部电影，并画出经过它们的不同时间无差异曲线。 （10 分）
假设 JB 是参数 δ = 0.9 和 β = 0 的朴素双曲线折扣器。他最终会看哪部电影？ (10 分)
假设 JB 是一个复杂的双曲线折扣器，参数 δ = 0.9 和 β = 0。他最终会看哪部电影？ (10 分)
Problem 3 (10pts)
Suppose Player 1 is a male player, player 2 is a female player.
Assume that player 1 is a level-2 male player, player 2 is a level-4 female player. Suppose that in the real world, level-0 male player tends to choose B, level-0 female player tends to choose C. What is the prediction of the game? Explain.
Problem 4 (30pts)
- Suppose Joanne is presented with a box filled with 60 colored tickets. Joanne knows that 20of them are black, 40 of them are either blue or green. Suppose Joanne is invited to randomly draw a ticket from the She is offered the following gambles: (A) if the ticket is black, she gets $10.
(B) If the ticket is green, she gets 10. (C) If the ticket is either black or blue, she gets $10. (D) If the ticket is either blue or green, she gets $10.
Draw a table for the four gambles. Point out which column corresponds to “sure thing.” Suppose Joanne prefers (B) to (A) and she prefers (D) to (C). Does she violates the sure-thing principle? (10 pts)
- Pleaseprovide an example of your own on preferences over (10 pts)
- Explain what probability weighting means. (10pts)
译文：问题三（10分） 电子商务
假设玩家 1 是男性玩家，玩家 2 是女性玩家。
假设玩家1是2级男玩家，玩家2是4级女玩家。假设在现实世界中，0 级男性玩家倾向于选择 B，0 级女性玩家倾向于选择 C。游戏的预测是什么？解释。
问题4（30分）
假设 Joanne 收到一个装满 60 张彩色票的盒子。 Joanne 知道其中 20 个是黑色的，其中 40 个是蓝色或绿色的。假设 Joanne 被邀请从她被提供的以下赌博中随机抽取一张票：(A) 如果票是黑色的，她得到 10 美元。
(B) 如果票是绿色的，她得到 10。(C) 如果票是黑色或蓝色，她得到 10 美元。 (D) 如果票是蓝色或绿色，她得到 10 美元。
为四场赌博画一张桌子。指出哪一列对应于“确定的事情”。假设乔安妮更喜欢 (B) 到 (A) 而她更喜欢 (D) 到 (C)。她是否违反了万无一失的原则？ （10 分）
请提供您自己的偏好示例（10 分）
解释概率加权的含义。 (10 分)
Problem 5 (40pts)
- Consider the following game table. Numbers in the table represent monetary
1a) Suppose both players only care about monetary payoffs. Find if any player has a strictly dom- inated strategy. What is the prediction of the game if both players never play strictly dominated strategies? (5 pts)
1b) Suppose that player 1 has Utilitarian preferences. That is, she cares about her own mone- tary payoff plus player 2’s monetary payoff. Player 2 has spiteful preferences with a spiteful level of 1. That is, he cares about his own monetary payoff minus player 1’s monetary payoff. Draw the corresponding new game table, circle the best responses and find the pure Nash equilibria. (15pts)
- Cosider the following game tree. Numbers in the tree represent monetary
2a) Suppose both players only care about monetary payoffs. Find the subgame perfect equilibria. (5 pts)
2b) Suppose that player 1 has Rawsian social preference. That is, she cares about the mini- mum payoff of the two players. Player 2 has altruistic preferences with a altruistic level of 0.5. That is, he cares about his own monetary payoff plus half of player 1’s monetary payoff. Draw the corresponding new game tree, find the subgame perfect equilibria. (15 pts)
译文：问题5（40分） 电子商务
考虑下面的游戏桌。表中数字代表货币
1a) 假设两个参与者都只关心货币收益。找出是否有任何玩家有严格支配的策略。如果两个玩家都从不使用严格支配的策略，对游戏的预测是什么？ （5 分）
1b) 假设玩家 1 有功利主义偏好。也就是说，她关心自己的金钱回报加上参与者 2 的金钱回报。玩家 2 有恶意偏好，恶意级别为 1。也就是说，他关心自己的货币收益减去玩家 1 的货币收益。画出相应的新游戏表，圈出最佳反应并找出纯纳什均衡。 (15 分)
考虑以下博弈树。树中的数字代表货币 电子商务
2a) 假设两个参与者都只关心货币收益。求子博弈完美均衡。 (5 分)
2b) 假设玩家 1 具有 Rawsian 社会偏好。也就是说，她关心两个参与者的最低回报。玩家 2 具有利他主义偏好，利他主义水平为 0.5。也就是说，他关心的是自己的货币收益加上玩家 1 的货币收益的一半。绘制相应的新博弈树，找到子博弈完美均衡。 （15 分）
Problem 6 (20 pts)
Suppose Kristine’s value function is given by v(x) = √2x for gains (x ≥ 0) and v(x) = −√−3x for losses (x < 0). Kristine is facing the choice between option (A) a sure amount $140 and option (B) a gamble which gives Kristine $200 with probability 0.6 and $50 with probability 0.4.
- If Kristine uses $0 as her reference point, what are the values of the two options? Which option would Kristine prefer? Draw the graph of Kristine’s value function, point out the values corresponding to the two options on the graph. (10pts)
- If Kristine uses $140 as her reference point, what are the values of the two options? Which option would Kristine prefer? Draw the graph of Kristine’s value function, point out the values corresponding to the two options on the graph. (10pts)
译文：问题 6（20 分）电子商务
假设 Kristine 的价值函数由 v(x) = √2x 给出，收益 (x ≥ 0) 和 v(x) = −√−3x 损失 (x < 0)。 Kristine 面临着在选项 (A) 确定的 140 美元和选项 (B) 之间的选择，赌博给 Kristine 200 美元的概率为 0.6 和 50 美元的概率为 0.4。
如果 Kristine 使用 $0 作为她的参考点，那么这两个选项的值是多少？ Kristine 更喜欢哪个选项？ 画出克里斯汀的价值函数图，指出图上两个选项对应的值。 (10 分)
如果 Kristine 使用 140 美元作为她的参考点，那么这两个选项的价值是多少？ Kristine 更喜欢哪个选项？ 画出克里斯汀的价值函数图，指出图上两个选项对应的值。 (10 分)
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