midterm2 2008 solutions

We can easily see that player 2 also does not want to

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Unformatted text preview: es and plays Lion his present payoff is 0 + 3δ/(1 − δ). Hence, player 1 does not want to deviate. We can easily see that player 2 also does not want to deviate in the P1 mode. If he plays Lion his present value payoff is 4 + 3δ/(1 − δ ), while if he deviates and plays chicken his present value payoff is 3 + 3δ/(1 − δ ). 3) Consider the infinitely repeated game with the following stage game (Linear Bertrand duopoly). Simultaneously, Firms 1 and 2 choose prices p1 ∈ [0, 1] and p2 ∈ [0, 1], respectively. Firm i sells ⎧ if pi < pj ⎨ 1 − pi (1 − pi ) /2 if pi = pj qi (p1 , p2 ) = ⎩ 0 if pi > pj units at price pi , obtaining the stage payoff of pi qi (p1 , p2 ). (All the previous prices are observed, and each player maximizes the discounted sum of his stage payoffs with discount factor δ ∈ (0, 1).) For each strategy profile below, find the range of parameters under which the strategy profile is a subgame­perfect equilibrium. a) (10 points) They both char...
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