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G AME T HEORY S ECOND D OSE : R EPEATED G AMES These are actually static games repeated several times. All the stages are identical and independent. We want to study how repeated interaction among players affects their strategic interactions. The key role of repeated interaction is that players are aware there is a future, for either rewarding (nice friendly behavior) or punishing (unfriendly one). For example, gas stations are involved in a daily pricing game. We want to analyze the impact of repetition on the prediction of the game. How does the long-run rivalry affect our predictions? In a one shot game we had quite a gloomy forecast about the performance of sellers, like gasoline stations, selling identical goods, constant marginal costs and competing in price. We predicted they would compete so aggressively that they would get no profits. I. Repetition for finitely many periods Suppose we repeat the Pricing game or a Prisoner's Dilemma twice. How is the prediction affected? Player 2 Do not Conf Conf Player 1 Do not Conf -1 , -1 -5,0 Conf 0,-5 -4 , -4 Nothing really happens. Let's see why. There is a final stage after which the game is over. What is your prediction for that final stage of the game? No matter what happened before we have a single prediction. History is a bygone, we are analyzing the usual one-shot game. Now go backwards. ..
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On the other hand let's try the following game: Player 2 L M R L 1 , 1 5 , 0 0 , 0 Player 1 M 0 , 5 4 , 4 0 , 0 R 0 , 0 0 , 0 3 , 3 Notice that (M,M) is not a NE of the one-shot (static) game. But, can we achieve (M,M), at least in the first stage? We now (M,M) cannot take place in the second period. Why? But, can players get to cooperate, and improve their profits, for a while at least (in the first period)? Check the following strategy: Play M in the first stage. In the second stage play R if (M,M) took
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