Prisoner’s dilemma

An exercise in calculating economic outcomes by means of 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 trust among strangers - for very good example, when unacquainted participants buy or sell in an unregulated market. This field developed into game theory.

The original dilemma

Pay-off table	A cooperates	A defects
B cooperates	A gets 1 year B gets 1 year	A goes free B gets 3 years
B defects	A gets 3 years B goes free	A gets 2 years B gets 2 years

Two people are charged with a conspiracy. 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:
  • A will not be prosecuted at all and will go free
  • B will be convicted of the main charge and will get 3 years in prison.
• If A informs B and B informs on A:
  • A will get 2 years in prison
  • B will get 2 years in prison
• If A refuses to inform on B and B refuses to inform on A:
  • A 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

eBayer’s dilemma payoff table'	Buyer cooperates	Buyer defects
Seller cooperates	Buyer gets £50 Seller gets £50	Buyer gets £150 Seller gets -£50
Seller defects	Buyer gets -£100 Seller gets £150	Buyer gets £0 Seller gets £0

The consequence is easier to see in more familiar context. Strangers consider a settling a transaction they have agreed on eBay to purchase a set of complete boxeed set of the final season of Some Mothers Do ’Ave ’Em on VHS, for £100. 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).

Single round

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.

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?

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.

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 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.

See also

• I believe