## 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:
## 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:
## 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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