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Pri­soner’s Dilemma

TagLast edit: 30 Sep 2020 19:08 UTC by Ruby

The Prisoner’s Dilemma is a well-studied game in game theory, where supposedly rational incentive following leads to both players stabbing each other in the back and being worse off than if they had cooperated.

The original formulation, via Wikipedia:

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. 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 only one year in prison (on the lesser charge).

The “stay silent” option is generally called Cooperate, and the “betray” option is called Defect. The only Nash Equilibrium of the Prisoner’s Dilemma is both players defecting, even though each would prefer the cooperate/​cooperate outcome.

Notice that it’s only if you treat the other player’s decision as completely independent from yours, if the other player defects, then you score higher if you defect as well, whereas if the other player cooperates, you do better by defecting. Hence Nash Equilibrium to defect (at least if the game is to be played only once), and indeed, this is what classical causal decision theory says. And yet—and yet, if only somehow both players could agree to cooperate, they would both do better than if they both defected. If the players are timeless decision agents, or functional decision theory agents, they can.

A popular variant is the Iterated Prisoner’s Dilemma, where two agents play the Prisoner’s Dilemma against each other a number of times in a row. A simple and successful strategy is called Tit for Tat—cooperate on the first round, then on subsequent rounds do whatever your opponent did on the last round.

External links

See also

References

In­tro­duc­tion to Pri­son­ers’ Dilemma

Scott Alexander30 Jun 2012 0:54 UTC
52 points
6 comments5 min readLW link

The Pavlov Strategy

sarahconstantin20 Dec 2018 16:20 UTC
209 points
13 comments4 min readLW link
(srconstantin.wordpress.com)

The True Pri­soner’s Dilemma

Eliezer Yudkowsky3 Sep 2008 21:34 UTC
136 points
115 comments4 min readLW link

2014 iter­ated pris­oner’s dilemma tour­na­ment results

tetronian230 Sep 2014 21:23 UTC
94 points
57 comments6 min readLW link

Pri­son­ers’ Dilemma with Costs to Modeling

Scott Garrabrant5 Jun 2018 4:51 UTC
111 points
20 comments7 min readLW link

Pri­soner’s Dilemma Tour­na­ment Results

prase6 Sep 2011 0:46 UTC
149 points
171 comments11 min readLW link

Ro­bust Co­op­er­a­tion in the Pri­soner’s Dilemma

orthonormal7 Jun 2013 8:30 UTC
114 points
146 comments7 min readLW link

Clas­sify­ing games like the Pri­soner’s Dilemma

philh4 Jul 2020 17:10 UTC
82 points
25 comments6 min readLW link
(reasonableapproximation.net)

Black­mail, Nukes and the Pri­soner’s Dilemma

Stuart_Armstrong10 Mar 2010 14:58 UTC
25 points
20 comments2 min readLW link

Co­op­er­at­ing with agents with differ­ent ideas of fair­ness, while re­sist­ing exploitation

Eliezer Yudkowsky16 Sep 2013 8:27 UTC
79 points
45 comments4 min readLW link

A Differ­ent Pri­soner’s Dilemma

Serpent-Stare14 Apr 2018 15:54 UTC
9 points
1 comment5 min readLW link

The Dar­win Game—Rounds 1 to 2

lsusr11 Nov 2020 1:53 UTC
48 points
9 comments3 min readLW link

Spe­cial­ized La­bor and Coun­ter­fac­tual Compensation

philh14 Nov 2020 18:13 UTC
18 points
2 comments19 min readLW link
(reasonableapproximation.net)

The Mu­tant Game—Rounds 11 to 30

lsusr23 Nov 2020 9:20 UTC
5 points
3 comments5 min readLW link

The Mu­tant Game—Rounds 31 to 90

lsusr27 Nov 2020 21:05 UTC
18 points
1 comment1 min readLW link

Con­trite Strate­gies and The Need For Standards

sarahconstantin24 Dec 2018 18:30 UTC
121 points
5 comments4 min readLW link
(srconstantin.wordpress.com)

Do­main The­ory and the Pri­soner’s Dilemma: FairBot

Gurkenglas7 May 2021 7:33 UTC
14 points
5 comments2 min readLW link

Co­or­di­nat­ing the Unequal Treaties

lsusr25 Nov 2021 10:47 UTC
23 points
2 comments2 min readLW link

Real World Solu­tions to Pri­son­ers’ Dilemmas

Scott Alexander3 Jul 2012 3:25 UTC
60 points
88 comments7 min readLW link

Pri­soner’s Dilemma (with visi­ble source code) Tournament

AlexMennen7 Jun 2013 8:30 UTC
68 points
236 comments2 min readLW link

The Epistemic Pri­soner’s Dilemma

MBlume18 Apr 2009 5:36 UTC
64 points
46 comments2 min readLW link

Pri­soner’s dilemma tour­na­ment results

AlexMennen9 Jul 2013 20:50 UTC
49 points
124 comments1 min readLW link

The con­tinued mi­suse of the Pri­soner’s Dilemma

SilasBarta23 Oct 2009 3:48 UTC
33 points
70 comments2 min readLW link

Paper: Iter­ated Pri­soner’s Dilemma con­tains strate­gies that dom­i­nate any evolu­tion­ary opponent

mapnoterritory2 Jun 2012 20:50 UTC
39 points
19 comments2 min readLW link

Fixed-Length Selec­tive Iter­a­tive Pri­soner’s Dilemma Mechanics

Andreas_Giger13 Sep 2011 3:24 UTC
34 points
14 comments15 min readLW link

Pri­soner’s Dilemma on game show Golden Balls

atorm21 Apr 2012 0:31 UTC
27 points
32 comments1 min readLW link

The Coun­ter­fac­tual Pri­soner’s Dilemma

Chris_Leong21 Dec 2019 1:44 UTC
20 points
15 comments3 min readLW link

The Truly Iter­ated Pri­soner’s Dilemma

Eliezer Yudkowsky4 Sep 2008 18:00 UTC
26 points
85 comments1 min readLW link

Pri­soner’s Dilemma as a Game The­ory Laboratory

prase25 Aug 2011 14:30 UTC
22 points
47 comments3 min readLW link

[LINK] Can­tor’s the­o­rem, the pris­oner’s dilemma, and the halt­ing problem

Qiaochu_Yuan30 Jun 2013 20:26 UTC
22 points
9 comments1 min readLW link

New­comb’s Prob­lem vs. One-Shot Pri­soner’s Dilemma

Wei_Dai7 Apr 2009 5:32 UTC
14 points
16 comments1 min readLW link

Reflex­ive Or­a­cles and su­per­ra­tional­ity: pris­oner’s dilemma

Stuart_Armstrong24 May 2017 8:34 UTC
14 points
2 comments4 min readLW link

Pri­soner’s Dilemma vs the Afterlife

DataPacRat24 Sep 2013 16:59 UTC
19 points
69 comments2 min readLW link

Other pre­spec­tive on re­solv­ing the Pri­soner’s dilemma

Stuart_Armstrong4 Jun 2013 16:13 UTC
17 points
34 comments1 min readLW link

Another Iter­ated Pri­soner’s Dilemma Tour­na­ment?

Andreas_Giger25 May 2012 14:16 UTC
14 points
23 comments1 min readLW link

The True Epistemic Pri­soner’s Dilemma

MBlume19 Apr 2009 8:57 UTC
18 points
72 comments2 min readLW link

New pris­oner’s dilemma and chicken tournament

benelliott14 Sep 2011 8:00 UTC
10 points
13 comments2 min readLW link

Agent-Si­mu­lates-Pre­dic­tor Var­i­ant of the Pri­soner’s Dilemma

Gram_Stone15 Dec 2015 7:17 UTC
11 points
34 comments2 min readLW link

Iter­ated Pri­soner’s Dilemma in soft­ware patents

RolfAndreassen22 Jul 2013 20:22 UTC
6 points
8 comments2 min readLW link

Pavlov Generalizes

abramdemski20 Feb 2019 9:03 UTC
64 points
4 comments7 min readLW link

Player of Games

Jacob Falkovich29 Aug 2018 21:26 UTC
52 points
3 comments12 min readLW link

Re-for­mal­iz­ing PD

cousin_it28 Apr 2009 12:10 UTC
32 points
63 comments2 min readLW link

[Question] A way to beat su­per­ra­tional/​EDT agents?

Abhimanyu Pallavi Sudhir17 Aug 2020 14:33 UTC
5 points
13 comments1 min readLW link

An­nounc­ing the 2014 pro­gram equil­ibrium iter­ated PD tournament

tetronian231 Jul 2014 12:24 UTC
38 points
63 comments1 min readLW link

Most Pri­soner’s Dilem­mas are Stag Hunts; Most Stag Hunts are Schel­ling Problems

abramdemski14 Sep 2020 22:13 UTC
131 points
31 comments10 min readLW link

The Dar­win Game

lsusr9 Oct 2020 10:19 UTC
88 points
136 comments3 min readLW link

Fair­ness vs. Goodness

Eliezer Yudkowsky22 Feb 2009 20:22 UTC
15 points
21 comments1 min readLW link

The Dar­win Game—Rounds 21-500

lsusr21 Nov 2020 0:58 UTC
27 points
16 comments2 min readLW link

In­tu­itions about utilities

mingyuan6 Feb 2021 0:12 UTC
31 points
3 comments4 min readLW link
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