3. Consider a modified Stackelberg model with three firms. The market inverse demand is given as P (Q) = a-bQ where Q=q1+92 +93. Each firm has a constant marginal cost c with no fixed cost. Assume a > c> 0 and 6 > 0. Answer the following questions only for pure strategies. (a) Find a set of subgame perfect Nash equilibria given the following timeline. Stage 1. Firm 1 chooses quantity qi≥ 0. Stage 2. After observing q₁, firms 2 and 3 simultaneously choose q2 ≥ 0 and 930, respectively. (b) Find a set of subgame perfect Nash equilibria given the following timeline. Stage 1. Firm 1 chooses quantity q1 ≥ 0. Stage 2. After observing 91, firm 2 chooses q2 ≥ 0. Stage 3. After observing q1 and q2, firm 3 chooses q3 ≥ 0.

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Chapter1: Making Economics Decisions
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3. Consider a modified Stackelberg model with three firms. The market inverse
demand is given as P (Q) = a-bQ where Q=q1+92 +93. Each firm has a constant
marginal cost c with no fixed cost. Assume a > c> 0 and 6 > 0. Answer the
following questions only for pure strategies.
(a) Find a set of subgame perfect Nash equilibria given the following timeline.
Stage 1. Firm 1 chooses quantity qi≥ 0.
Stage 2. After observing q₁, firms 2 and 3 simultaneously choose q2 ≥ 0 and
930, respectively.
(b) Find a set of subgame perfect Nash equilibria given the following timeline.
Stage 1. Firm 1 chooses quantity q1 ≥ 0.
Stage 2. After observing 91, firm 2 chooses q2 ≥ 0.
Stage 3. After observing q1 and q2, firm 3 chooses q3 ≥ 0.
Transcribed Image Text:3. Consider a modified Stackelberg model with three firms. The market inverse demand is given as P (Q) = a-bQ where Q=q1+92 +93. Each firm has a constant marginal cost c with no fixed cost. Assume a > c> 0 and 6 > 0. Answer the following questions only for pure strategies. (a) Find a set of subgame perfect Nash equilibria given the following timeline. Stage 1. Firm 1 chooses quantity qi≥ 0. Stage 2. After observing q₁, firms 2 and 3 simultaneously choose q2 ≥ 0 and 930, respectively. (b) Find a set of subgame perfect Nash equilibria given the following timeline. Stage 1. Firm 1 chooses quantity q1 ≥ 0. Stage 2. After observing 91, firm 2 chooses q2 ≥ 0. Stage 3. After observing q1 and q2, firm 3 chooses q3 ≥ 0.
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