經(jīng)濟(jì)學(xué)笑話：哪只輪胎爆胎？

40. Which Tire Was Flat?

Two guys were taking a Game-Theory class from a very boring Economics professor. They did pretty well on all of the quizzes and the midterms and assignments, and felt that they had a solid A's going into the final exam.

These two friends were so confident that they decided to go partying with some friends the weekend before the early Monday morning exam. So they did this and had a great time. However, with their hangovers and everything, they overslept all day Sunday and didn't make it 【1】 back to school until Monday afternoon.

They contacted the professor and explained to him why they missed the final. They told him that they had planned to come back in time 【2】 to take exam, but that they had a flat tire on the way back and didn't have a spare and couldn't get help for a long time and so were late getting back to campus. They asked to take the final the following morning. The professor thought this over and then agreed that they could make up 【3】 the final on the following day. The two guys were elated and relieved.

So, they studied that night and went in the next day at the time that the professor had told them. He placed them in separate rooms and handed each of them a test booklet and told them to begin. They looked at the first problem, which was something simple about Prisoner's Dilemma and was worth 5 points. "Cool!" they thought, "this is going to be easy." They did that problem and then turned the page. They were unprepared, however, for what they saw on the next page.

It said: (95 points) Which tire?

哪只輪胎爆胎？

兩個(gè)小伙子跟隨一位講課非常單調(diào)的經(jīng)濟(jì)學(xué)教授學(xué)習(xí)博弈論。他們都很出色地完成了所有的小測(cè)試、中期考試以及課外作業(yè)，他們覺得在馬上就要進(jìn)行的期末考試中準(zhǔn)能得優(yōu)。

這兩位朋友信心十足，于是決定在這個(gè)周末出去和朋友們聚會(huì)一番，而期末考試將在下周一一大早舉行。他們周末出去聚了會(huì)，玩得很開心。但是由于喝醉了酒，就在外面住了一晚，并且星期天一整天都在睡覺，直到周一下午才趕回了學(xué)校。

他們聯(lián)系上了教授，解釋了錯(cuò)過期末考試的原因。他們告訴教授原本計(jì)劃能夠趕回來參加考試的，但是在回來的路上汽車爆胎了，又沒有備用輪胎，而且很長(zhǎng)時(shí)間得不到幫助，因此很晚才趕回校園。他們請(qǐng)求教授讓他們?cè)倏家淮?。教授想了一?huì)，然后同意讓他們第二天上午補(bǔ)考。兩個(gè)小伙子興高采烈，如釋重負(fù)。

于是他們挑燈夜戰(zhàn)，加緊復(fù)習(xí)，第二天在教授說好的時(shí)間找到了他。教授把他們安排在不同的房間里，發(fā)給每人一套卷子，告訴他們開始作答。他們看到了第一個(gè)問題，那是一道關(guān)于囚徒困境的簡(jiǎn)單問題，只有5分。“太棒了！”他們暗想，“這次試卷不會(huì)很難。”他們做完了第一道題，然后翻到試卷的第二頁。第二頁上的試題內(nèi)容出乎他們的意料之外。

上面寫道：（本題95分）請(qǐng)問爆胎的是哪一只輪子？

背景知識(shí)與點(diǎn)評(píng)

·博弈論中最經(jīng)典的案例就是“囚徒困境”，指的是兩個(gè)共犯被抓，但是警察并沒有抓住他們犯罪的證據(jù)，于是把他們分別關(guān)在不同的房間里進(jìn)行審訊。審訊規(guī)則是，如果他們兩人同時(shí)承認(rèn)了犯罪，則犯罪事實(shí)清楚，他們被判有罪且被判入獄5年；如果兩人都不坦白，則警察證據(jù)不足，只能對(duì)他們各判2年；如果一方坦白而另外一方不坦白，則坦白從寬，坦白者被判1年，而不坦白者被重判7年。當(dāng)然，博弈的結(jié)果是兩人都坦白，盡管這個(gè)結(jié)果對(duì)兩人都不利。

·本笑話中的博弈論教授顯然受到了“囚徒困境”的啟發(fā)，于是也用類似“囚徒困境”的方法來考他的這兩位博弈論高材生，非常有意思。

·按常規(guī)他們開的汽車有四只輪子。答案一致，他們?cè)诘诙李}上就都會(huì)得到95分，得優(yōu)一點(diǎn)問題沒有。答案不一致，他們就每人只得5分，期末考試不及格。那么他們得優(yōu)的概率是多少呢？只有四分之一。

·更深入地探討一下，其實(shí)對(duì)于兩個(gè)學(xué)過博弈論的人來說，兩人得優(yōu)的概率還可以提高，這就用到了博弈論中“聚點(diǎn)均衡”（focus equilibrium）的概念：假如汽車四只輪子中最容易爆胎的是前面左邊的那只輪子（就像自行車的后胎比前胎更容易爆胎一樣），那么兩人就應(yīng)該都選擇前面左邊的那只輪子作為答案。

英語知識(shí)鏈接

【1】 make it：及時(shí)到達(dá)

【2】 in time：及時(shí)；適時(shí)

【3】 make up：彌補(bǔ)；償還