**Practice**Consider a market with three firms. Each firm has a different cost function.We assume C1(q1) = 7q1, C2(q2) = q2 + 1, and C3(q3) = 3q3. They compete by choosing prices a la Bertrand. The demand curve is Q(Pmin)20 Pmin. What is the aggregate market demand in the equilibrium, approximately?(a) 11=(b) 13(c) 15(d) 17(e) 19 =They compete by choosing quantities a la Cournot. The inverse demand is P(Q)33 2Q. What is the Nash equilibrium? Hint: don't go crazy on the math; try to solve theproblem by eliminating alternatives.(a) (91, 92, 93,=(3/2, 3/2,7/2)(b) (91, 92, 93) = (4, 1, 3)(c) (91, 92, 93)=(2,5,4)(d) (91, 92, 93) = (4,6,3)(e) (91,92,93) = (5/2,9/2, 10)

In oligopoly market structure, there are handful of suppliers and numerous buyers. Firms compete…

Answered: They compete by choosing prices a la…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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24. Two individuals play the following infinitely repeated prisoner's dilemma game: Player A Cooperate Defect Player B Cooperate 3,5 7,0 Defect 0,6 1, 1 Assume that both players discount future payoffs at rate 8<1. (a) If both players play 'cooperate' every period, then what are their total payoffs?
which is the nash equilibrium? small pig does press large pig does press (20, 130), small pig doesn't press large pig does press (140, 10), small pig does press large pig doesn't press (-5, 150), small pig does not press large pig doesn't press (0,0).
FOOP 6. (a) For the following extensive-form game: i. Identify the pure and mixed strategy Nash Equilibria. ii. Is the set of pure and mixed strategy Subgame Perfect Nash equilibria of the game different from the set of equilibria identified in part (a)? Explain (a couple of sentences should suffice). (3,1) A D B C (-2,-2) (2,5) D (0,7)
NE 2). Consider the following extensive form game between two players. (1,10) u D 1 B X (a) List all pure strategies of player 2. (b) Represent this game in normal form. (c) Find all pure-strategy Nash equilibria of this game. (d) Find all SPNE (in pure strategies) of this game. (6,3) (4,2) (5,1)
Problem 2. (SPNE 2). Consider the following extensive form game between two players. (1,10) .. D 2 1 B X Y (a) List all pure strategies of player 2. (b) Represent this game in normal form. (c) Find all pure-strategy Nash equilibria of this game. (d) Find all SPNE (in pure strategies) of this game. (6,3) (4,2) (5,1)
Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3 instead of 1: rock paper scissors rock 0. -3 1 1. раper scissors -1 -1 3 (a) Show that xT= (,) and yT= (5) together are not a Nash equilibrium 3'31 for this modified 3'3 game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.
rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.
MC Qu. 07-42 (Algo) Suppose Firm A and Firm... Suppose Firm A and Firm B are considering whether to invest in a new production technology. For each firm, the payoff to investing (given in thousands of dollars per day) depends upon whether the other firm invests, as shown in the accompanying payoff matrix. Firm A Don't Invest Invest Multiple Choice O What is the Nash equilibrium of this game? O Invest 9 for A 6 for B 7 for A 3 for B Firm B Firm A invests, and Firm B doesn't invest. Firm A invests, and Firm B invests. Not Invest 5 for A 7 for B Firm A doesn't invest, and Firm B invests. 12 for A 8 for B Firm A doesn't invest, and Firm B doesn't invest.
Ugly Dolls Inc. (UD) is a firm in Mytown that sells its products on a market under monopolistic competition. The cost function of UD is represented by TC = 100+10Q. Lately, because of the UD is making a big amount of profit, some firms enter the market to compete. If the number of firms entering the dolls market increase, we know that, 1. (a) The price of dolls will drop. (b) The average cost of UD will increase. (c) The quantity sold by UD will drop. (d) All the above answers are correct.
Firm 1 and Firm 2 compete in the same product market by setting quantities q₁ and 92, respectively. They have the same marginal cost c₁ = C₂ = 40. The market demand is p=1240 Q, where Q = 91 +92. 19. Suppose the game is played for one period. What are the equilibrium quantities? (a) q₁ = 1000, 92 1000 (b) q₁ = 800, q2 = 800 (c) 91 = 600, q2 = 600 (d) 9₁ = 400, q2 = 400 (e) 9₁ = 200, q2 = 200 In questions 19-21, suppose that this game is repeated for infinitely many periods. Firms have the same discount rate 8. Consider the situation in which the two firms are trying to implement a collusion scheme. With this intent, they employ the following grim-trigger strategy: in the first period, each firm produces the collusion quantity; from period two onwards, the firm keep producing the collusion quantity as long as no firm has ever pro- duced any quantity other than the collusion quantity; otherwise, the firm plays the Nash Equilibrium of the stage game. As you will see, what varies from one…
What is the payoff for both players in the SPNE of this game?-(2,5)-(3,4)- (2,2)- (5,1)- (1,7)
Consider the following game. Firm 1 can implement one of two actions, A or B. Firm 2 observes the action chosen by Firm 1 and then decides whether to fight it or not. (-10, 10) Firm 1 A B F2 • this strategy profile is F2 Fight Don't fight Fight Don't fight [Select] (20, 15) (a) Consider the following strategy profile: Firm 1 chooses A; Firm 2 chooses don't fight if A, and fight if B. (-10, 30) (25, 15) • this strategy profile i✓ [Select ] (b) Consider the following strategy profile: Firm 1 chooses A; Firm 2 chooses don't fight if A, and don't fight if B. • this strategy profile is [Select ] (c) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses fight if A and fight if B. not a Nash equilibrium a Nash equilibrium, but not a subgame perfect Nash equilibrium a subgame perfect Nash equilibrium none of the above

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