FinitelyRepeated

# FinitelyRepeated - Notes on Finitely Repeated Games Daniel...

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Unformatted text preview: Notes on Finitely Repeated Games Daniel Egel November 10, 2008 1 Starting off 1.1 Two-period Simple Prisoner’s Dilemma So lets start with the easiest type of finitely repeated game and then move forward. In particular lets start with a two-stage Prisoner’s dilemma where the game is given as: Firm 1 Firm 2 L H L 2, 2 8, 1 H 1, 8 4, 4 Now I’ll walk through the solution to the game. I’ll solve by backwards induction as we always do. • Lets start in the last (and second period). What happens in this period? It’s the last game that these two players will ever play so there is no chance in the future for punishment, rewarding for cooperation, etc. So how do they play? They play as if it was a one-shot static game: They play the Nash which is at { L, L } . • So now lets go to the first round (which is also the second to last round). What happens here? – All the players know that no matter what they choose in this period that they will play { L,L } in the next period. We showed this above. So we could rewrite this game as, Firm 1 Firm 2 L H L 4, 4 10, 3 H 3, 10 6, 6 where the new payoffs reflect the payoffs from the play in the first (current) round in addition to the (2 , 2) that they know that they will received in the next round. – How are the players going to play? They will play { L,L } in the current round. It is the unique Nash of this new game....
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FinitelyRepeated - Notes on Finitely Repeated Games Daniel...

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