博弈論 中的 囚徒困境

博弈論 中的 囚徒困境




之前幾次在網友處，提起 博弈論 中的 囚徒困境 論。


囚徒困境的主旨為：囚徒們雖然彼此合作，堅不吐實，可為全體帶來最佳利益（無罪開釋）。但在資訊不明的情況下，因為出賣同伙可為自己帶來利益（縮短刑期），也因為懷疑同伙可能把自己招出來，可為他帶來減刑利益，因此彼此互相出賣，雖違反最佳共同利益（無罪開釋），反而可能是自己謀求最大自身利益所在。


但實際上，執法機構不可能設立如此情境來誘使所有囚徒招供，因為囚徒們必須考慮刑期以外之因素（出賣同伙會在獄中及街頭受到報復等），而無法完全以執法者所設立之利益（刑期）作考量。


經典的囚徒困境如下：

警方逮捕甲、乙兩名嫌疑犯，但沒有足夠證據指控二人入罪。於是警方分開囚禁嫌疑犯，分別和二人見面，並向雙方提供以下相同的選擇：

若一人認罪並作證检控對方（相關術語稱「背叛」對方），而對方保持沉默，此人將即時獲釋，沉默者將判監10年。

若二人都保持沉默（相關術語稱互相「合作」），則二人同樣判監半年。

若二人都互相檢舉（互相「背叛」），則二人同樣判監2年。


用表格概述如下：


××××××××××××××甲沉默（合作）××××××××甲認罪（背叛）
乙沉默（合作）××二人同服刑半年××××××××甲即時獲釋；乙服刑10年
乙認罪（背叛）××甲服刑10年；乙即時獲釋××二人同服刑2年


「博弈論」看來像是很高深的學問，而其中的 「囚徒困境」論好像是犯罪心理學。不過其實是把人性加以深入研究罷了。


小學時代，記得是在小二，老師轉頭寫黑板時，聽到同學談話，遂要同學自己站出來，認罪否則全班一起罰企，老師把『保甲連坐』古為今用。初時沒有同學出聲，但不竟只得七八歲小孩，不多久就有二五仔，篤先前談話的同學出來，而那兩位談話的同學，亦不想見所有同學一同罰企，認了罪救了全班，之後做二五仔的那位同學，被全班杯葛整個月，而兩位敢於認罪的同學做了英雄。


又另有一次，已經是中一， 大家都有十二三歲， 那年當老師背著寫黑板時（其實是用Marker筆寫在百版上)，全班大部份同學，互射碼子，有一隻碼子誤中老師，大乜鑊！ 老師又是出『連坐』這一招，一係自首，否則全班要留堂。 大家已經十二三歲，懂得做男生要有『雷氣』，無人肯做二五仔，其實無人知道邊個射中老師，好了，老師下不了臺， 老羞成怒，放學後真的整班學生四十幾人，全班排隊去教員室罰企。


校車，保母車，白牌車，私家車司機們入來了解，發生了甚麼事，繼而通知家長，不久有部分家長們抵達，成百人塞在教員室裡面，連校長修士都驚動了，由修士樓上宿舍，落來睇下發生乜嘢事，真係慘，又要顧存老師面子，又要注重紀律，又要平釋事件，最後先放學生回家。 記得好像在期考這一科每人降一個 GRADE，但不用記過，真的還是假的無人知，亦無人續個去問，如果是真，無份射碼子的同學都幾冤枉。


博弈論(Game Theory)，有時也稱為對策論，或者賽局理論，電影
『A Beautiful Mind (film), 根據 A Beautiful Mind (book) 』本書拍成，就是講 博弈宗師，一九九四年 Nobel Memorial Prize in Economic Sciences Winner 諾貝爾獎 得獎者，John Nash 的經歷，阿尊一九二八年生，尚還在世。


人生本來就是一場博弈，選擇和被選擇，互相交替，成與敗，得或失，就像玩遊戲 Game 一場, 尚未釘蓋，都未能有最後定論！


本文已經寫好很久，儲起來等候機會登出。剛巧有網友講起『二五仔女』，『誅連』、『連坐』的古代執法，剩機出籠。




後記：


微豆兄 提出 Plea Bargaining 這個 Topic 與 囚徒困境 的博弈類同，但因為有了減刑的誘因，可以胡亂說謊把無辜的人拉入案件，增加自己的減刑機會。


【維基百科】Plea bargaining in the United States is very common; the vast majority of criminal cases in the United States are settled by plea bargain rather than by a jury trial.

They have also been increasing in frequency—they rose from 84% of federal cases in 1984 to 94% by 2001. Plea bargains are subject to the approval of the court, and different States and jurisdictions have different rules. Game theory has been used to analyze the plea bargaining decision.

The constitutionality of plea bargaining was established by Brady v. United States in 1970, although the Supreme Court warned that plea incentives which were sufficiently large or coercive as to over-rule defendants' abilities to act freely, or used in a manner giving rise to a significant number of innocent people pleading guilty, might be prohibited or lead to concerns over constitutionality. Santobello v. New York added that when plea bargains are broken, legal remedies exist.

Several features of the American justice system tend to promote plea bargaining. The adversarial nature of the system puts judges in a passive role, in which they are completely dependent upon the parties to develop the factual record and cannot independently discover information with which to assess the strength of the case against the defendant.

The parties thus can control the outcome of the case by exercising their rights or bargaining them away. The lack of compulsory prosecution also gives prosecutors greater discretion. And the inability of crime victims to mount a private prosecution and their limited ability to influence plea agreements also tends to encourage plea bargaining. Prosecutors have been described as monopsonists.

The shadow-of-trial argument states that plea agreements merely reflect the outcome that would have transpired had the case gone to trial. For example, if the accused faces 10 years and has a 50% chance of losing in court, then an agreement will result in a five-year sentence, less some amount deducted for saving the government the cost of trial.

Theoretically, the shadow-of-trial should work even better in criminal cases than in civil cases, because civil judgments are discretionary, while criminal judgments are often regulated by mandatory minima and sentencing guidelines, making sentences more predictable.

A counter-argument is that criminal sentencing laws are "lumpy", in that the sentencing ranges are not as precise as the dollars-and-cents calibration that can be achieved in civil case settlements. Furthermore, because some defendants facing small amounts of prison time are jailed pending trial, they may find it in their interests to plead guilty so as to be sentenced to time served, or in any event to end up serving less time than they would serve waiting for trial.

Outcomes in criminal cases are also made less predictable by the fact that, while a plaintiff in a civil case has a financial incentive to seek the largest judgment possible, a prosecutor does not necessarily have an incentive to pursue the most severe sentence possible.

The United States Supreme Court has recognized plea bargaining as both an essential and desirable part of the criminal justice system. The benefits of plea-bargaining are said to be obvious: the relief of court congestion, alleviation of the risks and uncertainties of trial, and its information gathering value.

However, in 1975 the Attorney-General of Alaska, Avrum Gross, ordered an end to all plea-bargaining; subsequent attorneys-general continued the practice. Similar consequences were observed in New Orleans, Ventura County, California, and in Oakland County, Michigan, where plea bargaining has been terminated.

Some legal scholars argue that plea bargaining is unconstitutional because it takes away a person's right to a trial by jury. In fact, Justice Hugo Black once noted that, in America, the defendant “has an absolute, unqualified right to compel the State to investigate its own case, find its own witnesses, prove its own facts, and convince the jury through its own resources. Throughout the process, the defendant has a fundamental right to remain silent, in effect challenging the State at every point to ‘Prove it!’” By limiting the powers of the police and prosecutors, the Bill of Rights safeguards freedom.

Plea bargaining is also criticized, particularly outside the United States, on the grounds that its close relationship with rewards, threats and coercion potentially endangers the correct legal outcome.

The theoretical work based on the prisoner's dilemma is one reason why, in many countries, plea bargaining is forbidden. Often, precisely the prisoner's dilemma scenario applies: it is in the interest of both suspects to confess and testify against the other suspect, irrespective of the innocence of the accused. Arguably, the worst case is when only one party is guilty—here, the innocent one is unlikely to confess, while the guilty one is likely to confess and testify against the innocent.

It has been argued that plea bargaining benefits society by ensuring that the guilty are not acquitted.

Another argument against plea bargaining is that it may not actually reduce the costs of administering justice. For example, if a prosecutor has only a 25% chance of winning his case and sending the defendant away to prison for 10 years, he may make a plea agreement for a one-year sentence; but if plea bargaining is unavailable, he may drop the case completely.



除了犯人可以用利用 Plea Bargaining 換取較短刑期，有時也會無辜被冤枉的可以被帶上法庭，牽涉入內的人要經過經年的法律程序，又要延聘律師付出金錢時間心力，家庭事業受到不必要的影響，最終才可以打甩罪名。



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