The Prisoner’s Dilemma and Strict Dominance

The prisoner’s dilemma is the most common introduction to new students of game theory. Two criminals are detained. The police suspect them of having conspired on a major crime but only have evidence of a minor crime. To charge them for the greater crime, they need to elicit a confession.

To do this, they lock the criminals in separate interrogation chambers and offer each of them the following deal. If both keep quiet, then they will each spend a minimal time in jail. If one confesses while the other keeps quiet, the police will let the rat go free while throwing the book at the silent one. If both confess, the testimony is no longer necessary, and so both will be charged for the larger crime—though the time in jail will not be as bad getting the book thrown at them.

Takeaway Points

  1. We solve the prisoner’s dilemma using the strict dominance solution concept.
  2. Strategy x strictly dominates strategy y for a player if x generates a greater payoff than y regardless of what the other players do.
  3. Strict dominance does not allow for equal payoffs. For example, suppose playing x and y both generated a payoff of 2 for an opposing strategy. Then x does not strictly dominate y.
  4. Rational players never play strictly dominated strategies. After all, why would you want to play a strategy that always does worse than something else?
  5. In a prisoner’s dilemma, confessing strictly dominates keeping quiet for both players. Thus, we expect both players to confess.
  6. The outcome of the game is inefficient. Both players would be better off if they both kept quiet instead. However, each player’s individual interest is to confess if they know that the other player will keep quiet. As such, silence is unsustainable.
  7. The conclusions of a game theory model produces are only as the assumptions built into it. Here, we assumed that players only wanted to minimize their own jail time. In practice, this might not be the case. For example, a mafia boss may kill a lieutenant who acts as an informant to the police. If we wanted to know what might happen in that sort of scenario, we would need to change the payoffs to accommodate that additional strategic concern.

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