Cournot Duopoly -- Nash Equilibrium
Cournot Duopoly -- Nash Equilibrium 3. Compute a Nash equilibrium of the Cournot-duopoly game when Remember...
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1. Find a Nash equilibrium for the peer-effects game in which u,(s,,s-i) =-(ai-Si)2-λ, . (s,-$2)2 for i = 1,2 Notice that the equilibrium will be a function of the given parameters 2. There are two...
7. Consider an asymmetric Cournot duopoly game, where the two firms have different costs of production. Firm 1 selects quantity qı at a pro- duction cost of 291. Firm 2 selects quantity 92 and pays the produc- tion cost 492. The market price is given by p = 12 – 91 - 92. Thus, the payoff functions are u(91,92) = (12 – 91 - 92.91 – 291 and uz(9192) = (12 – 91 - 92)92 – 492. Calculate the firms'...
5. Consider a version of the Cournot duopoly game, where firms 1 and 2 simul taneously and independently select quantities to produce in a market. The quantity selected by firm i is denoted q, and must be greater than or equal to zero, for i -1,2. The market price is given by p - 100 - 2q Suppose that each firm produces at a cost of 20 per unit. Further, assume that each firm's payoff is defined as its profit....
5. Consider a version of the Cournot duopoly game, which will be thoroughly analyzed in Chapter 10. Two firms (1 and 2) compete in a homogeneous goods market, where the firms produce exactly the same good. The firms simultaneously and independently select quantities to produce. The quantity selected by firm i is denoted q, and must be greater than or equal to zero, for i - 1,2. The market price is given by p-2 - q1 -q2. For simplicity, as...
1. Consider the following asymmetric version of the Cournot duopoly model. Two firms compete by simultaneously choosing the quantities (q, and q2) they produce. Their products are homogeneous, and market demand is given by p- 260-2Q, where Q-q +q2. Firm 1 has a cost advantage; Firm 1 produces at zero cost, while Firm 2 produces at a constant average cost of 40. (The difference in costs is what makes this an asymmetric game.) a. Derive both firms' profit functions, as...
Problem 2. Gibbons 1.5 Consider the following two finite versions of the Cournot duopoly model. First, suppose each firm must choose either half the monopoly quantity, 4m/2 = (a - c)/4, or the Cournot equilibrium quantity, 4c = (a - c)/3. No other quantities are feasible. Show that this two-action game is equivalent to the Prisoner's Dilemma: each firm has a strictly dominated strategy, and both are worse off in equilibrium than they would be if they cooperated. Second, suppose...
6. Entry Deterrence 2: Consider the Cournot duopoly game with demand p= 100 - (qı+q2) and variable costs c;(q;) = 0 for i € {1, 2}. The twist is that there is now a fixed cost of production k > 0 that is the same for both firms. Assume first that both firms choose their quantities simultaneously. Model this as a normal-form game. b. Write down the firm's best-response function for k = 1000 and solve for a pure-strategy Nash...
Write 2-4 sentences comparing the equilibrium you solved for with Cournot competition to the Nash equilibria we would solve for with simultaneous games in our game theory unit. Is a partial equilibrium with Cournot competition a Nash equilibrium? (3 points)
What is the Nash equilibrium for this game?
A.
A Nash equilibrium does not exist for this game.
B.
The Nash equilibrium is for Saudi Arabia to produce a low output
and Kuwait to produce a high output.
C.
The Nash equilibrium is for Saudi Arabia to produce a high
output and Kuwait to produce a high output.
D.
The Nash equilibrium is for Saudi Arabia to produce a low output
and Kuwait to produce a low output.
E.
The...
1. Statement 1: A Cournot Equilibrium is an example of a Nash Equilibrium where each frim selects its own prices. Statement 2: In Cournot Equilibrium as the number of firms increase, the price becomes closer and closer to the competitive equilibrium price. a. Both statements are true b. Both statements are false c. Statement 2 is true, but 1 is false d. Statement 1 is true, but 2 is false 3. Statement 1: In a Bertrand duopoly firms always want...