The Prisoner’s Dilemma constitutes a problem in game theory. In its classical model Prisoner’s Dilemma is presented as follows

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The Prisoner’s Dilemma constitutes a problem in game theory. In its classical model Prisoner’s Dilemma is presented as follows:

  • The Prisoner’s Dilemma constitutes a problem in game theory. In its classical model Prisoner’s Dilemma is presented as follows:

  • Hannah and Sam are interviewed

    separately.

  • They have the option to

    either cooperate or defect

    .


Model 1 – Player 1 plays ‘tit for tat’ as he is not sure Player 2 will act rationally.

  • Model 1 – Player 1 plays ‘tit for tat’ as he is not sure Player 2 will act rationally.

  • Model 2 – There is 2 sided uncertainty about stage payoffs.

  • Conclusion:

    • Although it is more beneficial for both players to co-operate, it cannot be guaranteed that it will occur in every single sequential equilibrium.



Assumptions:

  • Assumptions:

    • Game is repeated for a fixed number of times known to both players in advance.

    • Players act in a rational manner.

  • Conclusions:

    • Tacit co-operation > non co-operation.

    • Explained by player’s monetary incentive – incentive to gain utility from co-operation.

    • Results that don’t follow suit maybe justified by Krep’s idea of incomplete information of the other player’s payoff.



The paper suggested that

repeated prisoner’s dilemma is different from other Nash Equilibria.

  • The paper suggested that

    repeated prisoner’s dilemma is different from other Nash Equilibria.

  • Suggestions from the paper:

    • As the number of repetitions increases, the chance of co-operation increases.
    • Incomplete information about players’ opinions, motivations or behaviours can explain the observed co-operation.
  • Conclusions :

    If the players are restricted to using finite automata of a fixed size, then for a sufficiently large number of repetitions, there is an equilibrium that yields a payoff close to the co-operative one.



t

  • t

  • p

  • k

  • Probability that in round t a randomly chosen subject has intention to deviate periods 1 – k.

  • t k t

  • S = ∑ p

  • k m=1 m

  • Probability that in t the subject has intention to deviate.



  • Can co-operation ever be achieved in the finitely repeated Prisoner’s Dilemma?


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