Consider the following version of the Stackelberg duopoly in which a long-term firm competes with several short-term firms. The short-term firms are only on the market for a period while the long-term firm remains on the market for the entire duration of the game. In each stage game t, first the short-term firm fixes an amount xt. Then, the long-term firm observes xt and chooses a quantity yt. Then, both firms sell their quantities at the price pt = 1-(xt + yt). All firms have marginal costs equal to 0. The short-run firm maximizes its profit, which occurs at every t. For its part, the long-term firm maximizes the present value of the flow of benefits with a discount rate = 0.99At the beginning of each stage game, previously decided actions are common knowledge. 1. What is the subgame perfect equilibrium if the game is played a finite number of periods T? 2. Now consider the infinitely repeated version of this game. Find the subgame perfect equilibrium where x₁ = and yt = ½ in each period t. 3. Can you find a subgame perfect equilibrium in which xt = yt = 1/14 in each period t?

Consider the following version of the Stackelberg duopoly in which a long-term firm competes with several short-term firms. The short-term firms are only on the market for a period while the long-term firm remains on the market for the entire duration of the game. In each stage game t, first the short-term firm fixes an amount xt. Then, the long-term firm observes xt and chooses a quantity yt. Then, both firms sell their quantities at the price pt = 1-(xt + yt). All firms have marginal costs equal to 0. The short-run firm maximizes its profit, which occurs at every t. For its part, the long-term firm maximizes the present value of the flow of benefits with a discount rate = 0.99At the beginning of each stage game, previously decided actions are common knowledge. 1. What is the subgame perfect equilibrium if the game is played a finite number of periods T? 2. Now consider the infinitely repeated version of this game. Find the subgame perfect equilibrium where x₁ = and yt = ½ in each period t. 3. Can you find a subgame perfect equilibrium in which xt = yt = 1/14 in each period t?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.5P

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