EXPLORING ECONOMICS
8th Edition
ISBN: 2818000015614
Author: Sexton
Publisher: SAGE
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Question
Chapter 15, Problem 15P
To determine
To find:
The dominant strategy for the given payoff matrix.
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Use the strictly dominant strategy to find a Pure Strategy Nash Equilibrium if there is one.
Consider the Normal Form Game characterized in the following figure:
P1\P2 X Y Z
A
B
с
(1,1) (0,0) (-1,0)
(0,0) (2,2) (0,0)
(0,-1) (0,0) (3,3)
Which is the Strictly Dominated Strategy for player 1?
O (1,0,0)
O (0,1,0)
O (0,0,1)
There are no strictly dominated strategies for player 1
Consider the two-stage, static game depicted in Figure 5.1 involving two companies that enter into
an agreement to maximize total profits. The payoffs in this game are in millions of dollars. The
optimal strategy for both firms is to:
Firm Y
A
C
(3, 3)
(1, 1)
(1, 1)
Firm X
(1, 1)
(5, 5)
(7, 4)
C
(1, 1)
(4, 7)
(6, 6)
Payoffs: (Firm X, Firm Y)
FIGURE 5.1
O Play B in stage 1 and stage 2.
O Play B in stage 1 and play A in stage 2.
O Play C in stage 1 and stage 2.
O Play B in stage 1 and play C in stage 2.
O Play C in stage 1 and play B in stage 2.
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- Consider a Cournot duopoly. The inverse demand function of the market is given by p = 10-Q, where p is the market price, and Q = 91 +92 is the aggregate output. The marginal costs of the two firms are C₁ 1 and C₂ = 4. = (a) Solve for the Nash equilibrium of the game including firm out- puts, market price, aggregate output, and firm profits. (b) Now suppose these two firms play a 2-stage game. In stage 1, they produce capacities 9₁ and 92, which are equal to the Nash equilibrium quantities of the Cournot game characterised by part (a). In stage 2, they simultaneously decide on their prices p₁ and P2. The marginal cost for each firm to sell up to capacity is 0. It is impossible to sell more than capacity. The residual demand for 10 Piāj if Pi > Pj firm ij, is Di (Pi, Pj) = 10-Pi 2 = if pipi. (Note, if Pi < Pj 10 - Pi here we assume that the efficient/parallel rationing applies). Prove that it is a Nash equilibrium of the second stage subgame that each firm charges the market clearing…arrow_forwardCournot duopoly game. There are two firms each with cost zero. Each firm chooses its output. The demand function is p(q) = 1- q1 - q2. Because the price is negative for q; > 1, we may take the strategy set of each player to be Ai -[0, 1]. The Nash equilibrium strategy profile is (а) (3, 3) (b) No Nash equilibrium (c) (1/2, 1/2) (d) (1/3, 1/3)arrow_forwardFind all the Subgame Perfect Nash equilibrium of the game presented in Figure 1. D (7,-1) P2 E (3,0) A F (4,2) X (6,1) G B P2 (5,0) P1 P1 H X (-2,0) C (1,1) Figure 1: Extensive form game I (4,2) P2 K (1,3) J P1 (3,1)arrow_forward
- A total of n ≥ 2 companies are considering entry into a new market. The cost of entry is 30. If only one company enters, then its gross profit is 200. If more than one company enters, then each entrant earns a gross profit of 40. The payoff to a company that enters is its gross profit minus its entry cost, while the payoff to a company that does not enter is 60. Find a symmetric Nash equilibrium in mixed strategies.arrow_forwardProblem 5.1. The inverse market demand for printer paper is given by P = 400 – 2Q. There are two firms who compete to produce this paper, each with a marginal cost of production equal to c = 40 over a large range of output (ie, assume constant marginal cost). The two firms compete in quantities, in other words they each simultaneously choose a quantity to produce (Cournot competition). Derive the Cournot-Nash equilibrium of this game. Please write final answers in the boxes, showing work in blank areas. (a) The reaction function for each firm. 91 (92): 92 (91) (b) Optimal output q for each firm. 92 = р = = π1 = (c) Market price (from demand curve). (d) Firm profits. 92 = π2 =arrow_forwardTwo identical firms are engaged in Cournot competition, with cost functionsTCA(QA) = 10 QA and TCB(QB) = 10 QB. The market demand is given by P = 610 –2Q.a) Plot the best response functions and report the Cournot-Nash equilibrium quantities, price and profits.b) What are the prices, quantities, and profits for the firms if they decide to collude and share profits equally? c) Show that firms have an incentive the deviate from the collusive outcome.d) Find the Stackelberg equilibrium if A leads and B follows.e) Show the equilibria in the previous parts on the inverse demand function. Calculate and identify consumer surplus and deadweight loss in each equilibrium..arrow_forward
- where is the nash equilibrium? find out the dominant strategy. it was discovered that two domestic manufacturing companies were fixing prices. if each company is silent, there is no penalty, but production and business are disrupted due to continuous investigation by the Fair Trade Commission. The penalty for revealing the estimated loss due to the investigation and collusion is as follows: Firm 2 Silence Disclosure Silence -200, -200 -590, 0 Firm 1 Disclosure 0, -590 -450, -450 fine( a hundred million won)arrow_forwardTwo firms are considering simultaneously developing a new product for a market. The costs of developing the product are $10m but there will only be revenue in the market of $40m if only one of the firms develops the product. If both firms develop the product then earnings/revenues will be competed away. a) Capture this entry game in a payoff matrix. b) What is the Nash equilibrium and why? Please provide explanation. c) Does either firm have a dominant strategy? Please provide explanation.arrow_forwardExercise 6.7. Suppose two identical companies produce wood stoves and they are the only ones on the market. Its costs are given by: C1 (q1 )=200q1 and C2 (q2) = 200q2. And the inverse market demand curve is: P=2000-2Q, where Q =q1 + q2 Get the Cournot-Nash equilibrium. Calculate the profits of each company. Show graphically. Suppose that the two companies form a cartel to maximize joint profits. How many stoves will you produce? Calculate the profits of each company. Represent graphically. Managers now note that explicit agreements to collude are illegal. Each company must decide on its own whether to produce the amount of Cournot or that of the cartel.arrow_forward
- Two firms A and B produce a product jointly. The total value to the two firms from the joint venture is given by V = √iA + √iB where iA and iB are the firms’ respective investment levels. After the investment levels have been chosen, the firms divide V equally. a) Find the Nash equilibrium investment levels, and the payoffs for each firm. b) Suppose that A and B merge. Find the optimal investment levels and the payoffs for the merged firm. Do the firms benefit from the merger? Why?arrow_forwardConsider an oligopoly market with 3 firms. They face a demand curve given by p(Q) = 300 – 5Q, where Pmin refers to the lowest price offered by any firm. The marginal costs are the following: C₁ = : 80, C₂ 210. The fixed costs for each firm are zero and firms compete a la Bertrand. Which of the following is consistent with a Nash equilibrium of this game? € refers to the minimal price change possible. = (a) Pmin (b) Pmin (c) Pmin (d) Pmin (e) Pmin = 80 and only firm 1 sells. 200, C3 - 190 and only firm 1 sells. = = 200 - € and only firm 1 sells. 200 and firms 1 and 2 sell. - = = 210 and all firms sell.arrow_forwardthe answer IS NOT A)arrow_forward
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