Suppose that there are two profitmaximizing firms (firm 1 and firm 2). Each firm chooses its...
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Suppose that there are two profitmaximizing firms (firm 1 and firm 2). Each firm chooses its output (q. 20 for firm 1 and 92 20 for firm 2) to maximize its profit. Each firm can produce any amount of output costlessly (i.e. total cost is zero for each firm). The inverse demand function is p(q) = 62q and where q = 91 +92 is the total output produced for the market. Question 1 (10 points): Solve for the Nash Equilibrium if the firms move simultaneously. Ignore boundary solutions in which either q₁0 or 92 = 0. Question 2 (10 points): Solve for the Subgame Perfect Nash Equilibrium (SPNE) if the game is played sequentially: firm 1 moves first (choosing q) and then firm 2 chooses q2 after firm 2 sees q₁. Ignore boundary solutions in which either ₁ = 0 or 9₂ = 0. Question 3 (10 points): Suppose that the stage game is the simultaneousmove game described in Question 1. However, this stage game is repeated infinitely many times. Suppose that each player has a discount rate 6, where 0 ≤6<1. Recall that and that What is the weakest condition on 6, if any, such that the following strategy profile is a SPNE to the infinitely repeated game? • Player 1 chooses g₁ = 1/2 in any period if 9₁ = = 1/2 in all previous periods • Player 1 chooses q = 3/2 in any period if either q period 1/2 or 2 1/2 in any previous • Player 2 chooses (2 = 1/2 in any period if q=2= 1/2 in all previous periods •Player 2 chooses 2 = 3/2 in any period if either q1 1/2 or 2 1/2 in any previous period Suppose that there are two profitmaximizing firms (firm 1 and firm 2). Each firm chooses its output (q. 20 for firm 1 and 92 20 for firm 2) to maximize its profit. Each firm can produce any amount of output costlessly (i.e. total cost is zero for each firm). The inverse demand function is p(q) = 62q and where q = 91 +92 is the total output produced for the market. Question 1 (10 points): Solve for the Nash Equilibrium if the firms move simultaneously. Ignore boundary solutions in which either q₁0 or 92 = 0. Question 2 (10 points): Solve for the Subgame Perfect Nash Equilibrium (SPNE) if the game is played sequentially: firm 1 moves first (choosing q) and then firm 2 chooses q2 after firm 2 sees q₁. Ignore boundary solutions in which either ₁ = 0 or 9₂ = 0. Question 3 (10 points): Suppose that the stage game is the simultaneousmove game described in Question 1. However, this stage game is repeated infinitely many times. Suppose that each player has a discount rate 6, where 0 ≤6<1. Recall that and that What is the weakest condition on 6, if any, such that the following strategy profile is a SPNE to the infinitely repeated game? • Player 1 chooses g₁ = 1/2 in any period if 9₁ = = 1/2 in all previous periods • Player 1 chooses q = 3/2 in any period if either q period 1/2 or 2 1/2 in any previous • Player 2 chooses (2 = 1/2 in any period if q=2= 1/2 in all previous periods •Player 2 chooses 2 = 3/2 in any period if either q1 1/2 or 2 1/2 in any previous period
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Related Book For
Fundamentals of Heat and Mass Transfer
ISBN: 9780471457282
6th Edition
Authors: Incropera, Dewitt, Bergman, Lavine
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