Suppose Player 1 and Player 2 plan to go to either a football match (F), or a concert (C) in the evening.  Players 1 and 2 are away from each other during the day and neither know which event the other is going to go to.  By the evening, Players 1 and 2 are both either happy or upset independently of each other.  Player 1 only knows that Player 2 is happy with probability 0.3 and upset with probability 1-0.3.  Player 2 only knows that Player 1 is happy with probability 0.5 and upset with probability 1-0.5.  Each player knows with certainty whether they themsleves are happy or upset.
假设玩家 1 和玩家 2 计划在晚上去看一场足球比赛 （F） 或一场音乐会 （C）。 玩家 1 和 2 白天彼此远离，谁也不知道对方要参加哪个活动。 到了晚上，玩家 1 和 2 要么高兴，要么彼此不高兴。 玩家 1 只知道玩家 2 对概率 0.3 感到满意，对概率 1-0.3 感到不安。 玩家 2 只知道玩家 1 对 0.5 的概率感到满意，对 1-0.5 的概率感到不安。 每个玩家都肯定地知道他们是高兴还是沮丧。

If both players are happy, the utilities of each player given their choice of event are given in the payoff matrix:                           
如果两个玩家都满意，则每个玩家在选择事件时的效用都会在收益矩阵中给出：

If Player 1 is happy but Player 2 is upset, the utilities of each player given their choice of event are given in the payoff matrix:
如果玩家 1 很高兴，但玩家 2 不高兴，则每个玩家选择的事件的效用将在收益矩阵中给出：

If Player 1 is upset but Player 2 is happy, the utilities of each player given their choice of event are given in the payoff matrix:
如果玩家 1 不高兴，但玩家 2 高兴，则每个玩家选择的事件的效用都会在收益矩阵中给出：

Finally if both players are upset, the utilities of each player given their choice of event are given in the payoff matrix:
最后，如果两个玩家都心烦意乱，则每个玩家在选择事件时的效用都会在收益矩阵中给出：

In the ex-ante normal form game associated with this Bayesian game, what is the expected utility of Player 1 if Player 1 chooses the strategy FF (i.e., F if happy and F if unhappy) and Player 2 chooses the pure strategy CC?  Round your answer to two decimal places.
在与此贝叶斯博弈相关的事前正态博弈中，如果玩家 1 选择策略 FF（即 F 如果快乐，F 如果不快乐）并且玩家 2 选择纯策略 CC，那么玩家 1 的预期效用是什么？将您的答案四舍五入到小数点后两位。

Suppose Player 1 and Player 2 plan to go to either a football match, or a concert in the evening.  Players 1 and 2 are away from each other during the day and neither know which event the other is going to go to.  By the evening, Players 1 and 2 are each either happy or upset independently of each other.  Player 1 only knows that Player 2 is happy with probability 0.1 and upset with probability 1-0.1.  Player 2 only knows that Player 1 is happy with probability 0.1 and upset with probability 1-0.1.  Each player knows with certainty whether they themselves are happy or upset.  Denote choosing to go to the football match by F, and choosing to go to the concert by C.
假设玩家 1 和玩家 2 计划在晚上去看一场足球比赛或一场音乐会。 玩家 1 和 2 白天彼此远离，谁也不知道对方要参加哪个活动。 到了晚上，玩家 1 和 2 各自独立地感到高兴或沮丧。 玩家 1 只知道玩家 2 对概率 0.1 感到满意，对概率 1-0.1 感到不安。 玩家 2 只知道玩家 1 对概率 0.1 感到满意，对概率 1-0.1 感到不安。 每个玩家都肯定地知道他们自己是高兴还是沮丧。 F表示选择去看足球比赛，C表示选择去看演唱会。

If both players are happy, the utilities of each player given their choice of event are given in the payoff matrix:                           
如果两个玩家都满意，则每个玩家在选择事件时的效用都会在收益矩阵中给出：

If Player 1 is happy but Player 2 is upset, the utilities of each player given their choice of event are given in the payoff matrix:
如果玩家 1 很高兴，但玩家 2 不高兴，则每个玩家选择的事件的效用将在收益矩阵中给出：

If Player 1 is upset but Player 2 is happy, the utilities of each player given their choice of event are given in the payoff matrix:
如果玩家 1 不高兴，但玩家 2 高兴，则每个玩家选择的事件的效用都会在收益矩阵中给出：

Finally if both players are upset, the utilities of each player given their choice of event are given in the payoff matrix:
最后，如果两个玩家都心烦意乱，则每个玩家在选择事件时的效用都会在收益矩阵中给出：

In the ex-ante normal form game associated with this Bayesian game, what is the expected utility of Player 2 if both players choose the pure strategy CF (i.e., C if happy and F if unhappy)?  Round your answer to 2 decimal places.
在与此贝叶斯博弈相关的事前正态博弈中，如果两个玩家都选择纯策略 CF（即 C 如果高兴，则 F 不高兴），玩家 2 的预期效用是什么？将您的答案四舍五入到小数点后 2 位。

Consider a second price auction for a single item with two bidders. Suppose bidder 1 has a value uniformly drawn in the interval from 0 to 1, while bidder 2 has a value 0.9.
考虑对一件物品进行第二次价格拍卖，其中有两个投标人。假设投标人 1 的值在 0 到 1 的区间内均匀绘制，而投标人 2 的值为 0.9。

In the Bayesian equilibrium in undominated strategies, what is the seller's expected revenue? Give your answer to two decimal places.
在非主导策略的贝叶斯均衡中，卖方的预期收入是多少？把你的答案给出两个小数位。

Two firms simultaneously decide whether to Enter (E) or stay out (O). The state of the market can be strong or weak and it is known by Firm 1 only. Firm 2 believes that a strong and a weak state are equally likely.
两家公司同时决定是进入（E）还是退出（O）。市场状态可强可弱，只有公司 1 知道。公司 2 认为强国和弱国的可能性相同。

Letting Firm 1 be the row choser, the payoffs when the market is weak are:
让公司 1 成为行选择者，当市场疲软时的回报是：

The payoffs when the market is strong are: 
市场强劲时的回报是：

The ex-ante normal form associated with this Bayesian game is:
与此贝叶斯博弈相关的事前正态形式为：

Consider the extensive form game with imperfect imformation below.  In this game, Player 2 is weak with probability and strong with probability 1-.
考虑下面信息不完美的广泛形式游戏。在这个游戏中，玩家 2 的概率 较弱，概率为 1- 的强。

Suppose = 3 and = -2 and suppose Player 1's strategy is to choose E.  What is the smallest probability for which this strategy is part of a subgame perfect equilibrium?  Round your answer to two decimal places.
假设 = 3 和 = -2，假设玩家 1 的策略是选择 E。该策略是子博弈完美均衡的一部分的最小概率 是多少？将您的答案四舍五入到小数点后两位。

Select all statements that are true.
选择所有为 true 的语句。

Amy (the row player) has just started dating Brad (column player). Each person can choose either to (C)ommit to the relationship, or (D)ump their partner and break up. Amy prefers a partner who will commit. Unfortunately, Amy knows there are two types of men in the world: Gentlemen and Playboys. She doesn’t yet know Brad's type, but from experience, she assigns probability 3/4 to Brad being a Playboy and probability 1/4 that he is a Gentleman. Brad knows his own type. The payoffs for each action and type profile are given as follows:
艾米（排球员）刚刚开始和布拉德（列球员）约会。每个人都可以选择（C）省略这段关系，或者（D）拒绝他们的伴侣并分手。艾米更喜欢一个愿意承诺的合作伙伴。不幸的是，艾米知道世界上有两种类型的男人：绅士和花花公子。她还不知道布拉德的类型，但根据经验，她认为布拉德是花花公子的概率为 3/4，他是绅士的概率为 1/4。布拉德知道自己的类型。每个操作和类型配置文件的收益如下：

Brad is a Playboy (probability 3/4):
布拉德是花花公子（概率 3/4）：

	Commit	Dump
Commit	3 , 0	3 , 3
Dump	0 , 3	0 , 3

Brad is a Gentleman (probability 1/4):
布拉德是个绅士（概率 1/4）：

	Commit	Dump
Commit	3 , 3	3 , 0
Dump	0 , 3	0 , 0

What is the unique Bayesian-Nash equilibrium of this game?
这个博弈独特的贝叶斯-纳什均衡是什么？

Consider the following Bayesian variant of the Bank Run game, where player 1 has one type and player 2 has two types
考虑以下 Bank Run 游戏的贝叶斯变体，其中玩家 1 有一种类型，玩家 2 有两种类型.

What is the minimum value of p such that Player 1 plays R in a pure strategy Bayesian Nash equilibrium?
玩家 1 在纯策略贝叶斯纳什均衡中扮演 R 的最小值是多少？

Garry and Ross are sales representatives for the same company. Their manager informs them that of the two of them, whoever sells more this year wins a new car. Each day, Garry and Ross privately decide how hard they will work for the day.
Garry 和 Ross 是同一家公司的销售代表。他们的经理告诉他们，在他们两个人中，今年卖得更多的人将赢得一辆新车。每天，Garry 和 Ross 都会私下决定他们当天的工作强度。

Select all features from the list below that MOST LIKELY apply to this situation. (Note: partial credit is possible for this question.)
从下面的列表中选择最有可能适用于这种情况的所有功能。（注意：这个问题可以部分学分。

Six thousand players each pay $10,000 to enter the World Series of Poker. Each starts the tournament with $10,000 in chips, and they play No‑ Limit Texas Hold ’Em (a type of poker) until someone wins all the chips. The top 600 players each receive prize money according to the order of finish, with the winner receiving more than $8,000,000.
六千名玩家每人支付 10,000 美元参加世界扑克系列赛。每个人都以 10,000 美元的筹码开始比赛，然后他们玩无限注德州扑克（一种扑克），直到有人赢得所有筹码。前 600 名选手按完赛顺序获得奖金，获胜者将获得超过 8,000,000 美元。

Select all features from the list below that MOST LIKELY apply to this situation. (Note: partial credit is possible for this question.)
从下面的列表中选择最有可能适用于这种情况的所有功能。（注意：这个问题可以部分学分。