Prisoner's dilemma - jaredgorski.org

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Prisoner's dilemma

Keywords: game-theory, non-cooperative game theory
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  • In game theory, the "Prisoner's dilemma" refers to a thought experiment where, given a particular game and set of rules, two players will select optimum individual strategies that actually present the worst outcome for both.

The scenario:

  • Given:

    • Prisoners A and B are:
      • charged with assault (a "lesser" charge)
        • Punishment (negative reward): 1 year in prison
      • suspected of armed robbery (a "more serious" charge)
        • Punishment (negative reward): 3 years in prison
    • Prisoners are not allowed to communicate
    • Prisoners are each faced with a decision between "snitching" on the other prisoner (betrayal, non-cooperation) in exchange for 1 year removed from their punishment or staying silent (cooperation)
      • Both prisoners are "Rational" (each will make the best choice to minimize their punishment given what they know)

      • If both prisoners betray each other, both serve 2 years in prison for armed robbery charge minus the 1 year removed for their betrayals

      • If one prisoner snitches and the other prisoner remains silent, the snitching (defecting/betraying) prisoner goes free and the silent (cooperative) prisoner serves all 3 years in prison for the more serious charge (armed robbery)

      • If both prisoners remain silent, they're both convicted of the lesser charge (assault) and serve 1 year in prison each

      • Payoff matrix:

        A \ B B silent B betrays
        A silent -1 \ -1 -3 \ 0
        A betrays 0 \ -3 -2 \ -2
  • Then:

    • Each player's best individual strategy (without knowing what the other player will do) is to betray the other, since it results in a best-case reward of going free and a worst-case reward of 2 years in prison (if betrayed)
    • This "best individual strategy" is actually the worst corporate/cooperative/coalitional strategy because it results in the greatest net punishment (negative reward): -4
    • The actual best strategy is for both players to cooperate, but the communication barrier between the players prevents them from "rationally" doing so, despite their best interests

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