Refer to the normal-form game of price competition in the payoff matrix below. Firm A Low Price High Price Firm B Low Price 0,0 -10, 50 High Price 50,-10 20, 20 What are the secure strategies for Firm A and Firm B? Firm A - High Price, Firm B - Low Price Firm A - High Price, Firm B - High Price Firm A - Low Price, Firm B - High Price Firm A - Low Price, Firm B - Low Price

Refer to the normal-form game of price competition in the payoff matrix below. Firm A Low Price High Price Firm B Low Price 0,0 -10, 50 High Price 50,-10 20, 20 What are the secure strategies for Firm A and Firm B? Firm A - High Price, Firm B - Low Price Firm A - High Price, Firm B - High Price Firm A - Low Price, Firm B - High Price Firm A - Low Price, Firm B - Low Price

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 8MC

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Consider a situation where two firms, 1 and 2, compete by choosing prices simultaneously. Theycan either compete (charge a low price) or cooperate (collude, charging a high price). The firmsplay this competition game repeatedly and indefinitely, using a grim trigger strategy toincentivize cooperation. They use the same interest rate, i, to discount future payoffs. Payoffsare $4,050 when both firms cooperate and $3,600 when they compete. If one firm charge a lowprice while the other charges a high price, the firm charging the low price gets $7,200, and theother gets zero, but now assume there is a 10% chance that aregulatory agency will give both firms a $1,500 fine in each period if they are caught colluding.Find the condition on the interest rate, i , necessary for sustaining the cooperative equilibrium.Which of the following statements is correct?(a) For any i < 1/7 the firms will cooperate.(b) For any i < 1/11 the firms will cooperate.(c) For any i > 1/11 the firms will…
Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.
Consider this market that is dominated by two airlines, American and United. Each can choose to charge a high price (and restrict capacity) or charge a low price (and expand capacity). If one of the airlines reduces the price and the other does not, then the airline that reduced the price can capture customers from the other airline. The profits for each outcome is shown below: a. Does United have a dominant strategy? If so, what is it? Explain. b. What is the Nash equilibrium in this game? Explain. c. Is this game an example of a Prisoner’s Dilemma? Explain.
Consider this market that is dominated by two airlines, American and United. Each can choose to charge a high price (and restrict capacity) or charge a low price (and expand capacity). If one of the airlines reduces the price and the other does not, then the airline that reduced the price can capture customers from the other airline. The profits for each outcome is shown below: a.Does United have a dominant strategy? If so, what is it? Explain. b. What is the Nash equilibrium in this game? Explain. c. Is this game an example of a Prisoner’s Dilemma? Explain.
Explain all will rate what is always true for a pure nash equilibrium of a two-person non zero-sum game A.No player can improve his payoff with a unilateral change of strategy B. it is a Pareto maximum of the payoff matrix C. No player can worsen the payoff of his opponent with a unilateral change of strategy D. It gives worse payoffs to both players than any berge equilibrium
Two farmers, Ali and Hasan, graze their animals on a common land. They canchoose to use the common resource lightly or heavily and the resulting strategic interactionmay be described as a strategic form game. The payoff matrix is the following: (The table is attached on iamges part) Suppose that the game is repeated infinitely. If both players play a Grim-Trigger strategy, findthe discount factor δ such that (Light,Light) be a Nash equilibrium
Refer to the payoff matrix in question 8 at the end of this chapter. First, assume this is a one-time game. Explain how the $60/$57 outcome might be achieved through a credible threat. Next, assume this is a repeated game (rather than a one-time game) and that the interaction between the two firms occurs indefifi nitely. Why might collusion with a credible threat not be necessary to achieve the $60/$57 outcome?
Consider the Cournot duopoly game with demand p = 100 − (q1+ q2) and variable costs ci(qi) = 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. a. 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 equilibrium. Is it unique? c. Now assume that firm 1 is a “Stackelberg leader” in the sense that it moves first and chooses q1. Then after observing q1 firm 2 chooses q2. Also assume that if firm 2 cannot make strictly positive profits then it will not produce at all. Model this as an extensive-form game tree as best you can and find a subgame-perfect equilibrium of this game for k = 25. Is it unique? d. How does your answer in (c) change for k = 225?
Refer to the normal-form game of price competition in the payoff matrix below. Suppose the game is infinitely repeated, and the interest rate is 10 percent. Both firms agree to charge a high price, provided no player has charged a low price in the past. (a) If both firms stick to this agreement, then what is the present value of firm A's payoffs? Please show your calculations. (b) If firm A cheats, what is the present value of the returns for Firm A for cheating? Please show your calculations.
a. Assume the game is played in one period. Using best responses, find all Nash equilibria. b. Now assume the game is played twice. For what discount values will both firms be willing to cooperate and play (A, A) in this first period and the higher value Nash equilibrium in the second period if one firm punishes any deviation by the other firm in the first period by playing the lower value Nash equilibrium in the second period?
The following payoff matrix depicts the profits for the only two firms in this oligopolistic industry. In each cell, the 1st number is Firm A’s profit and the 2ndnumber is Firm B’s Profit. (Scenario: Payoff Matrix for Firms A and B) In the scenario Payoff Matrix for Firms A and B. If they play the game for 10 times, what will be firm A's pay off if both A and B will choose "always choosing High price strategy", i.e the firm will always choose High price each time? 60 Need more information to tell. 100 6
True or False?: (Recall that a strategic game is called Dominance Solvable if and only if exactlyone action profile remains after iteratively eliminating all strictly dominated actions.)If a strategic game is dominance solvable, it can have at most one Nash equilibrium.