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 prisoner’s dilemma

If you play this game in isolation the payoff is grim: if you cooperate you get reamed. Your best interest is in informing on the other guy, because his best interest is in forming on you.

This look

See also

• I believe