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Prisoner’s dilemma (view source)

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An exercise in calculating economic outcomes by means of {{tag|metaphor}}, the prisoners dilemma was developed at the RAND corporation in the 1950s by those splendid brainboxes  as a way of predicting individuals’ behaviour in situations requiring [[I believe|trust]] among strangers - for very good example, when unacquainted participants buy or sell in an unregulated market. This field developed into [[game theory]].
{{a|bi|{{prisonersdilemmatable}}}}The [[prisoner’s dilemma]] is the mathematician’s way of articulating the [[commercial imperative]].


===The original dilemma===
An exercise in calculating economic outcomes by means of {{tag|metaphor}}, the [[prisoner’s dilemma]] was developed at the RAND corporation in the 1950s by those splendid brainboxes as a way of predicting individuals’ behaviour in situations requiring [[I believe|trust]] among strangers - for very good example, when unacquainted participants buy or sell in an unregulated market. This field developed into [[game theory]].
{{prisonersdilemmatable}}
 
==The original prisoner’s dilemma==
Two people are  charged with a conspiracy<ref>Whether or not they are guilty is beside the point. If it helps you empathise with their predicament, assume they’re innocent</ref>.  Each is held separately. They cannot communicate. There  is enough evidence to convict both on a lesser charge, but not the main charge. Each prisoner is separately offered the same plea bargain. The offer is:
Two people are  charged with a conspiracy<ref>Whether or not they are guilty is beside the point. If it helps you empathise with their predicament, assume they’re innocent</ref>.  Each is held separately. They cannot communicate. There  is enough evidence to convict both on a lesser charge, but not the main charge. Each prisoner is separately offered the same plea bargain. The offer is:
*If A informs B but B refuses to inform on A:
*If A informs B but B refuses to inform on A:
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**B will get 1 year in prison (on the lesser charge).
**B will get 1 year in prison (on the lesser charge).


===The [[eBayer’s dilemma]]===
Another way of looking at this, for those easily triggered, is as the [[eBayer’s dilemma]].
{{eBayer’s dilemma}}
The consequence is easier to see in more familiar context. This version {{author|Douglas Hofstadter}} once described as the "briefcase came", but Millennials will recognise it as the [[eBayer’s dilemma]].  
 
Strangers consider a settling a transaction they have drunkenly agreed on eBay to purchase a set of complete boxed set of the final season of ''Some Mothers Do ’Ave ’Em'' on VHS, for £100<ref>The eBayers don’t ''have'' to be drunk, but as we all know, most people on eBay ''are'', so this is a bit of dramatic colour.<r/ef>. The seller must pay and the buyer must post the videos simultaneously. Assume the Seller would have sold the videos at any price over £50 (so the transaction represents a £50 profit for her), and privately, the buyer would have been prepared to pay £150, (the transaction therefore representing a £50 profit for him).
 
When settling the transaction, each has the following risks:
*If the seller posts ''and'' the buyer pays:
**The seller will get £100 but will lose a video it values a £50 (+£50).
**the seller will get a video it values at £150 but must pay £100 (+50)
*If the seller posts, but the buyer does not pay:
**The buyer will have video it values at £150 for free (+£150)
**The seller has given away a video it values a £50 for nothing (-£50).
*If the buyer pays but the seller does not post:
**The buyer will have paid £100 for nothing (-£100)
**The seller will receive £150 and will still have the video it values a £50 (+£200).
*If the seller does not post ''and'' the buyer does not pay:
**The seller is in its original position (£0).
**The buyer is in its original position (£0).
 
 
{{ref}}


===Single round===
===[[Single round prisoner’s dilemma]]===
If you play this game in isolation — with someone you don’t know and whom you do not expect to meet again, the payoff is grim: those who cooperate will get reamed. Cooperation is a bad strategy. Your best interest is in defecting on the other guy, because ''his'' best interest is defecting on ''you''.  
If you play the game once, and in isolation — with someone you don’t know and whom you do not expect to meet again, the payoff is grim: those who cooperate will get ''reamed''. Cooperation is a bad strategy. Your best interest is in defecting on the other guy, because ''his'' best interest is defecting on ''you''.  


This looks like a bad outcome for commerce. If the rational disposition is to weasel on a deal, how can we have any faith in the market? How, come to think of it, has any kind of market ever got off the ground? Why would anyone take on a sure fire losing bet?
This looks like a bad outcome for commerce: if [[homo economicus]] ''should'' weasel on every deal, how can we have any faith in the market? How, come to think of it, has any kind of market ever got off the ground? Why would anyone take on a sure fire losing bet? Is this the smoking gun that homo economicus doesn’t exist?<ref>No. [[Homo economicus]] ''doesn’t'' exist, but this is not the reason why.</ref>


Because trust, faith and confidence changes everything. The single round prisoner’s dilemma stipulates there is ''no consequence'' on a bad actor for reneging. The defector is guaranteed to get away with it: these are the rules.
Because [[trust]], faith and confidence changes everything. The [[single round prisoner’s dilemma]] stipulates there is ''no consequence'' on a bad actor for reneging. The defector is guaranteed to get away with it: these are the rules.


But in real life, one-off interactions with strangers — counterparts whom you are guaranteed never to see again — are rare. Business is the process of cultivating relationships. Establishing trust.
But in real life, one-off interactions with strangers — counterparts whom you are certain never to see again — are extremely rare, especially in our interconnected age. Business is the process of cultivating relationships. Establishing [[trust]].


The game theorists found an easy way to replicate that concept of trust: run the same game again. Repeatedly. An indefinite amount of times.  
The game theorists found an easy way to replicate that concept of trust: run the same game again. Repeatedly. An indefinite amount of times.  This is the [[iterated prisoner’s dilemma]].


===“Iterated” [[prisoner’s dilemma]]===
===[[Iterated prisoner’s dilemma]]===
The same actors get to observe how each other act, and respond accordingly. If your counterpart defects, you have a means of retaliating: by defecting on the next game, or by refusing to play the game any more with that counterparty.
The same actors get to observe how each other act, and respond accordingly. If your counterpart defects, you have a means of retaliating: by defecting on the next game, or by refusing to play the game any more with that counterparty.


Now, as well as the short-term payoff, there is a longer-term payoff, and it ''dwarfs'' the short term payoff.  If I defect once, I earn £150. If I cooperate a thousand times, I earn £50,000. If I defect first time round, sure: I am £100 up, but at what cost: if my counterparty refuses to play with me again — and if she tells other players in the market — I will struggle to make much money. ''No one will trust me''.
Now, as well as the short-term payoff, there is a longer-term payoff, and it ''dwarfs'' the short term payoff.  If I defect once, I earn £150. If I cooperate a thousand times, I earn £50,000. If I defect first time round, sure: I am £100 up, but at what cost: if my counterparty refuses to play with me again — and if she tells other players in the market — I will struggle to make much money. ''No one will trust me''.


{{seealso}}  
===''One prisoner, or ''two''?===
In our view, one correctly places the apostrophe to designate a ''single'' prisoner having the dilemma — so [[prisoner’s dilemma]], not ''prisoners’'' dilemma — because both prisoners if taken together ''have'' no dilemma: it is only where they are acting individually that they have a problem ... ''with each other''.
{{sa}}  
*The [[tragedy of the commons]]
*[[Agency problem]]
*[[I believe]]
*[[I believe]]
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