Please help with this problem, Thank you =2. Consider a Cournot competition environment with one good and two firms, Firm 1 and Firm 2. The(pure) strategy space of Firm 1 is S₁ = [0, 1], and the strategy s₁ of Firm 1 corresponds to the amountof the good they produce. Similarly, the (pure) strategy space of Firm 2 is S₂ = [0,1], and the strategy82 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantityS₁ and Firm 2 were to produce quantity s2, the prevailing price in the good market would be 1-81 - 82,the utility of Firm 1 would be their profit, u₁ (S1, S2) = (1 − 81 S2 - c) s₁, and the utility of Firm 2would be their profit, u2 (81, 82) = (1- 81 - 82 - c) s2, where 0 ≤ c < 1 is the marginal cost of productionfor both firms.(a) Find the pure-strategy Nash equilibria of this game.(b) Are there other Nash equilibria in this game. Consider now a Bertrand competition environment with one good and two firms, Firm 1 and Firm 2.The (pure) strategy space of Firm 1 is S₁ [0, 5], and the strategy s₁ of Firm 1 corresponds to the=price they charge for the good. Similarly, the (pure) strategy space of Firm 2 is S2 [0,5], and thestrategy s2 of Firm 2 corresponds to the price they charge for the good. If Firm 1 were to choose priceS₁ and Firm 2 were to choose price s2, then the demand Firm 1 would face is given by1D1 ($1, $2)={if 81 82,if s₁ = 82,0if 81 82,the demand Firm 2 would face is given byif 82< S1,1D2 (81, 82)=if 82 = 81,0if 82 > $1,=the utility of Firm 1 would be their profit, u₁ (S1, S2) (811)D1 (S1, S2), and the utility of Firm 2would be their profit, u2 (81, 82) = (82 − 1)D2 (81, 82). (The marginal cost of production for both firmsis 1.)(c) Find the pure-strategy Nash equilibria of this game.-Consider now an altered version of the Bertrand competition environment above in which the (pure)strategy space of Firm 1 is S₁ = {0, 1, 2, 3, 4, 5}, the (pure) strategy space of Firm 2 is S₂ = {0, 1, 2, 3, 4, 5},and otherwise the game is the same as the Bertrand competition environment above.(d) Find the pure-strategy Nash equilibria of this game.

Given,Under Cournot modelUnder Bertrand model

2. Consider a Cournot competition environment with one good and two firms, Firm 1 and Firm 2. The (pure) strategy space of Firm 1 is S₁ = [0,1], and the strategy s₁ of Firm 1 corresponds to the amount of the good they produce. Similarly, the (pure) strategy space of Firm 2 is S₂ = [0, 1], and the strategy 82 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity s₁ and Firm 2 were to produce quantity s2, the prevailing price in the good market would be 1-81-82, the utility of Firm 1 would be their profit, u₁ (81, 82) = (1 - 81 - 82 - c) s₁, and the utility of Firm 2 would be their profit, u2(81, 82) = (1-81-82-c) s2, where 0 ≤ c < 1 is the marginal cost of production for both firms. (a) Find the pure-strategy Nash equilibria of this game. (b) Are there other Nash equilibria in this game.

2. Consider a Cournot competition environment with one good and two firms, Firm 1 and Firm 2. The (pure) strategy space of Firm 1 is S₁ = [0,1], and the strategy s₁ of Firm 1 corresponds to the amount of the good they produce. Similarly, the (pure) strategy space of Firm 2 is S₂ = [0, 1], and the strategy 82 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity s₁ and Firm 2 were to produce quantity s2, the prevailing price in the good market would be 1-81-82, the utility of Firm 1 would be their profit, u₁ (81, 82) = (1 - 81 - 82 - c) s₁, and the utility of Firm 2 would be their profit, u2(81, 82) = (1-81-82-c) s2, where 0 ≤ c < 1 is the marginal cost of production for both firms. (a) Find the pure-strategy Nash equilibria of this game. (b) Are there other Nash equilibria in this game.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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