QUESTION 7Firm 1 and Firm 2 are Stackelberg competitors. Firm 1 is the leader and Firm 2 is the follower. They have the same cost functions:Firm 1: C₁(Q1) = 4Q1Firm 2: C2(Q2) = 4Q2The market demand isQD = 46-0.5PCompute the SPE of this game.In equilibrium, Firm 1 produces Q₁=✓, Firm 2 produces Q2=✓, and the price is P=

Stackelberg is a sequential game. The leader chooses their quantity based on what the follower…

Firm 1 and Firm 2 are Stackelberg competitors. Firm 1 is the leader and Firm 2 is the follower. They have the same cost functions: Firm 1: C1(Q1) = 4Q1 Firm 2: C2(Q2) = 4Q2 The market demand is QD=46-0.5P Compute the SPE of this game. In equilibrium, Firm 1 produces Q₁= ✓, Firm 2 produces Q2= ✓, and the price is P=

Firm 1 and Firm 2 are Stackelberg competitors. Firm 1 is the leader and Firm 2 is the follower. They have the same cost functions: Firm 1: C1(Q1) = 4Q1 Firm 2: C2(Q2) = 4Q2 The market demand is QD=46-0.5P Compute the SPE of this game. In equilibrium, Firm 1 produces Q₁= ✓, Firm 2 produces Q2= ✓, and the price is P=

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter13: best-practice Tactics: Game Theory

Section: Chapter Questions

Problem 10E

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Suppose two Bertrand competitors, F1 and F2, make identical products for a market with inverse demand P = 600 – 0.5Q. Both firms have the same costs Ci = 20qi, and each firm has sufficient capacity to supply the entire market. a. What prices will the firms choose? How much might each produce and what profit would they make? Is the result a Nash equilibrium? Explain. b. Suppose F1 improves its efficiency, reducing its cost to C1 = 16q1. What will happen in this market? Explain. c. Assume now that the firms have their original identical costs, but that F1 has only 100 units of capacity and F2 has only 200 units of capacity. What prices will the firms choose now? Explain why neither firm will want to decrease its price at the equilibrium you identify. Why would neither firm want to increase its price? Prove this for F1.
1. Consider an industry with inverse demand given by p = 8 – q, where p is the price, and q is the quantity. There is one incumbent firm and one potential entrant. In the first stage of the game, the incumbent chooses its quantity qi. In the second stage, the potential entrant observes qi and chooses its quantity Ce. The potential entrant can also decide not to enter the market. The production technology of both firms are represented by the cost function C = 2q. To enter industry implies a fixed entry cost of F. (a) Find the equilibrium of the game, assuming that the potential entrant enters the industry. What are the profits of firms? (b) Assume that entry is not blockaded. For which values of F does the incumbent firm prefer to deter entry? (c) For which values of F, entry blockaded?
You are considering entering a market serviced by a monopolist. You currently earn £0 economic profits, while the monopolist earns £5. If you enter the market and the monopolist engages in a price war, you will lose £5 and the monopolist will earn £1. If the monopolist doesn't engage in a price war, you will each earn profits of £2. (a) Write out the extensive form of the above game? (b) Are there any Nash equilibria for the game? Explain. (c) Is there a subgame perfect equilibrium? Explain. (d) If you were the potential entrant, would you enter? Explain why or why not.
Consider the location game we covered in Lecture 3. Now assume there arethree players (vendors). As we assumed in the lecture, consumers in each area choosethe closest vendor and if there are multiple closest vendors then these vendors receiveequal share of consumers in the area. Notice Si = {1, 2, 3, ...., 9} for i = 1, 2, 3. Here aresome examples of payoffs: u1(1, 1, 1) = 3, u1(1, 1, 9) = u2(1, 1, 9) = 2.25, u3(1, 1, 9) =4.5, u1(1, 5, 9) = u3(1, 5, 9) = 2.5 and u2(1, 5, 9) = 4. (a) Is s′1 = 1 strictly dominated by s′′1 = 2 for player 1?(b) Is s′1 = 1 weakly dominated by s′′1 = 2 for player 1?(c) Can you find a Nash equilibrium in pure strategies?
Someone please clear my doubt.I have posted question and got answer,i attached the ques and ans(refer image). I can't understand how q1=19800 and q2=0 in equilibrium when the two actors have the same cost and revenue functions and they act simultaneously in a one-shot game. Intuitively one would guess that a cournot equillibrium would occur when q1=q2. Am I wrong i assuming that there can be no "player business that chooses to produce first" in a one-shot simultaneous game? What am i not understanding?
Consider a quantity-setting duopoly. The two firms are Alpha, Ltd. and Beta, Inc. The demand schedulein this market is: p Qd180 150155 175130 200Each firm has a constant marginal cost of 30 per unit. Suppose each firm can choose to produce either 75units or 100 units. Firms make their quantity choices simultaneously and the market price is whatever itneeds to be to sell the total output in the market.(a) Draw up the normal form game matrix, showing the players, strategies, and payoffs. Show your workdetermining the profits in each box in the matrix.(b) Determine the Nash equilibrium of this game.(c) Suppose the firms were able to come to an agreement to make more profit. What would this agreementbe?(d) Explain how the government might respond to such an agreement and why.
Consider a quantity-setting duopoly. The two firms are Alpha, Ltd. and Beta, Inc. The demand schedulein this market is:p Qd180 150155 175130 200Each firm has a constant marginal cost of 30 per unit. Suppose each firm can choose to produce either 75units or 100 units. Firms make their quantity choices simultaneously and the market price is whatever itneeds to be to sell the total output in the market.(a) Draw up the normal form game matrix, showing the players, strategies, and payoffs. Show your workdetermining the profits in each box in the matrix.(b) Determine the Nash equilibrium of this game.(c) Suppose the firms were able to come to an agreement to make more profit. What would this agreementbe?(d) Explain how the government might respond to such an agreement and why
Economics - Game Theory & Business Strategy Inverse Market Demand for tires is P = 200 - .01Q We assume the manufacturer sets a Price, 'X', for the tires and the manufacrturer moves first, selecting 'X' before any sales decisions are made. In this variation, we assume there are 3 retail firms, each with Market Power. The firms (1,2,3) make their sales decisions (q1,q2,q3) simultaneously, taking the manufacturer's price X as given. Total market sales, Q, then equal q1 + q2 + q3. We assume the only cost for the retailers is the cost 'X' for each tire. Additionally, the manufacturer produces the tires at a Marginal Cost of $10 a tire. **** Write out the Extensive form of this game ****
(a) Assuming that each fishery chooses fi ∈ (0,F), to maximize its payoff function, derive the players’ best response functions and find a Nash equilibrium. (b) Is the equilibrium you found in (a) unique or not? What are equilibrium payoffs? (c) Suppose that a benevolent social planner wants maximize the util- ity of both fisheries. In other words, the social planner solves the following problem: max w(f1, f2) = u1(f1, f2) + u2(f1, f2) (f1 ,f2 )= 2ln(f1)+2ln(f2)+2ln(F −f1 −f2). Find the social planner’s solution. (d) What are the fisheries’ payoffs if the quantities of fish they catch are solutions to the social planner’s problem? What can you say about the Nash equilibrium quantities of fish being caught as compared to the social planner’s solution? (e) If fishery j decides to follow the recommendation of the social planner, how much fish will firm i catch?
6 Two people will select a policy that affects both of them by applying a "veto" in a sequential and alternate manner, that is: person 1 begins to veto a policy and then person 2 exercises his "veto" with the remaining policies; the process repeats until only one policy remains. Assume that there are 3 policies: X,Y,Z, and that person 1 prefers X to Y to Z and person 2 prefers Z to Y to X. a. Represents the game extensively b. Give the number of subgames C. Indicate the total strategies of the players d. find all subgame perfect nash equilibria e. Find all Nash Equilibriums.
Consider a modified Traveler’s Dilemma. In terms of strategy options that the players have and the dollars they earn, it is like the standard Traveler’s Dilemma, but the players do not have endless appetite for money. Up to 100 dollars, each dollar feels like a dollar. But any moneybeyond 100 is psychologically like 100 dollars. Assuming that players are maximizers of ‘psychological’ dollars instead of real dollars, describe all the Nash equilibria of this modified Traveler’s Dilemma.
13) Two identical firms are engaged in Cournot competition, with cost functionsTCA(QA) = 30 QA and TCB(QB) = 30 QB. The market demand is given by P = 480 –3Q.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 consumersurplus and deadweight loss in each equilibrium. If you can only answer a limited amount of questions, please answer d and e :)