Prisoner’s Dilemma

William Poundstone in his 1993 book Prisoner’s Dilemma as:

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don’t have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain.

The possible outcomes are:

  • If A and B each betray the other, each of them serves two years in prison
  • If A betrays B but B remains silent, A will be set free and B will serve three years in prison
  • If A remains silent but B betrays A, A will serve three years in prison and B will be set free
  • If A and B both remain silent, both of them will serve one year in prison (on the lesser charge).

It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision by itself will not affect their reputation in the future. As betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other, even though mutual cooperation would yield greater reward.
In this case, “to betray” is the dominant strategy for both players, meaning it is the player’s best response in all circumstances, and it is aligned with the Sure-thing principle. The prisoner’s dilemma also illustrates that the decisions made under collective rationality may not necessarily be the same as that made under individual rationality, and this conflict can also be witnessed in a situation called “Tragedy of the Commons”. This case indicates the fact that public goods are always prone to over-use.

2 thoughts on “Prisoner’s Dilemma

  1. shinichi Post author


    ウィリアム・パウンドストーンは、1993年に書いた「囚人のジレンマ : フォン・ノイマンとゲームの理論」のなかで、次のような例を挙げている(年数は異なる)。


    • 本来ならお前たちは懲役5年なんだが、もし2人とも黙秘したら、証拠不十分として減刑し、2人とも懲役2年だ。
    • もし片方だけが自白したら、そいつはその場で釈放してやろう(つまり懲役0年)。この場合黙秘してた方は懲役10年だ。
    • ただし、2人とも自白したら、判決どおり2人とも懲役5年だ。




    囚人Bが「黙秘」を選んだ場合、自分 (=囚人A) の懲役は2年(「黙秘」を選んだ場合)か0年(「自白」を選んだ場合)だ。だから「自白」を選んで0年の懲役になる方が得だ。
    囚人Bが「自白」を選んだ場合、自分 (=囚人A) の懲役は10年(「黙秘」を選んだ場合)か5年(「自白」を選んだ場合)だ。だからやはり「自白」を選んで5年の懲役になる方が得だ。





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