Consider a repeated prisoner’s dilemma game that will be repeated for one million rounds. 1. If...

Consider a repeated prisoner’s dilemma game that will be repeated for one million rounds.

1. If this game is played by immortal rational utility maximizers, what is the Nash equilibrium for this repeated game?

2. If this game was played as an experiment using human players, would you expect to see this strategy?

3. If this game was played as an experiment with rational utility maximizers who have a maximum lifespan of 500,000 rounds, what is the Nash equilibrium for this repeated game?

Expert Solution

A typical prisoner dilemma's payoff matrix is given as follows:

Nash equilibrium of this game is (Confess, Confess)

If this game is repeated for one million rounds,

1)

For a finite horizon game played by immortal rational utility maximizers, Nash equilibrium of this repeated game is still

(Confess, Confess) (moving back through the logic of backward induction and presence of a dominant strategy). Also one million is very large number but theoretically results for immortal rational utility maximizers will only change for an infinite horizon game.

2)

If this game was played as an experiment using human players, we would not expect (Confess, Confess) as an equilibrium solution in each round. With one million rounds at hand, human players will most likely develop a coordinated strategy and choose (Lie, Lie) increasing both of their payoffs.

3)

If this game was played as an experiment with rational utility maximizers who have a maximum lifespan of 500,000 rounds but game horizon is 1 million rounds, this means for this rational utility maximizers, it is essentially an infinite repeated game. The Nash equilibrium of this repeated game is (Lie, Lie) with punishment strategy such as grim trigger or tit-for-tat in case one of the prisoner's deviate from this equilibrium.

Rahul Sunny answered 1 year ago

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