midterm2 2008 solutions

In the cooperation mode according to the strategy

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Unformatted text preview: iple to check if this is a SPE. In the cooperation mode according to the strategy profile both players will always play Chicken. This yields present value of 3/(1 − δ ) to each player. If player i deviates in period t and plays Lion, his payoff increases to 4 in that period. In period t + 1, according to the strategy profile they go to P i mode. In P i mode player i plays Chicken while the other player plays Lion. Then in the next period they go back to the Cooperation mode. This yields a present value of 4 + 1δ + 3δ 2 /(1 − δ ). Players don’t want to deviate if 3/(1 − δ ) > 4 + 1δ + 3δ2 /(1 − δ ) ⇔ δ > 1/2.Since P1 and P2 modes are symmetrical we only have to verify for one of these modes. In mode P1 player 1 plays Chicken while the other player plays Lion. This is a NE of the stage game. Since in the next period they go back to the Cooperation mode regardless of the actions, neither player wants to deviate. If player 1 does not deviate his present payoff is 1 + 3δ/(1 − δ ). If he deviat...
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