Macmillan Learning Oligopoly and Game Theory: End of Appendix Problem Cat and mouse is a simple game in which each player can choose either Right or Left. If the cat and mouse both choose Right or both choose Left, that is very bad for the mouse but good for the cat. If the cat and mouse choose different strategies that is good for the mouse but not good for the cat. The Nash Equilibrium in this cat and mouse game is
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Step 1: In this game, the Nash Equilibrium occurs when both players choose the strategy that is best for them given the strategy chosen by the other player. Show more…
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3. Suppose the market for widgets (a fictitious good) is characterized by an infinitely repeated oligopoly game (notice I have not given you any details on the game itself). A monopolist in this market would earn $12 million each period, but the current market is comprised of four (4) suppliers, each of whom earn $1 million per period in the Nash equilibrium of the one-shot game. Collusion is illegal, and these are honest, law-abiding firms. Nevertheless, they recognize their own interdependence. If the firms had somehow agreed to collectively produce the monopoly level of output, they all know that a firm who defects from that agreement would earn $4 million that period. Supposing that each of the players were to play a trigger strategy, compute the value of alpha above which such a strategy, when played by all firms, would represent a Nash equilibrium of the infinitely repeated game. Your answer should be a decimal between 0 and 1, rounded to the third decimal place (e.g. 0.768).
Supreeta N.
The following matrix shows strategies and payoffs for two firms that must decide how to price. Firm 2 Price High Price Low Firm 1 Price High 400, 400 -50, 700 Price Low 700, -50 100, 100 Entrant Enter Don't enter Monopolist Price High 20, 10 50, 0 Price Low 5, -10 10, 0 a) Is the monopolist's threat to charge a low price credible? That is, if the entrant has come in, would it make sense for the monopolist to charge a low price? Explain. b) What is the Nash equilibrium of this game? c) How could the monopolist make the threat to fight credible?
Nick J.
Consider a duopoly market where firms compete in quantities and with the following cost function and demand curve: MC=ATC=160, P=2000−10Q. What is firm 1’s reaction function? What is firm 2’s reaction function? What are each firm’s quantities at the Cournot equilibirum? What is the price at the Cournot equilibrium? What are each firm’s profits at the Cournot equilibrium? Suppose the two firms discuss forming a cartel. f. What price should the cartel set? If the firms split the market evenly, how much should the each produce? g. What profits do each firm make under the agreement in (f)? h. Suppose firm 1 sticks to the agreement, but firm 2 best responds to firm 1’s quantity. How many units does firm 2 make and what are their profits? i. Show this strategic situation as a normal form game, where each firm has two actions: Cartel (C) or Best Respond (BR). Use the payoffs you have calculated to populate the game and calculate any missing values. What is the Nash Equilibrium of the game?
Akash M.
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