Prisoner’s dilemma

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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[1]. 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

References

  1. Whether or not they are guilty is beside the point. If it helps you empathise with their predicament, assume they’re innocent