Consider the game below: Player C Q-50 Q-100 Q-150 Player R Q-50 37.37 30.40 20.37 Q-100 40,30 Q-150 37.20 32.32 15.25 25.15 0.0 Where player R's payoff is written first. What is the equilibrium in the game? Select one: a. In equilibrium, both firms choose Q = 50. b. There are two equilibria, associated with the (40,30) payoff and the (30,40) payoff. c. The only equilibrium is in mixed strategies. d. In equilibrium, both firms choose Q = 100.

Consider the game below: Player C Q-50 Q-100 Q-150 Player R Q-50 37.37 30.40 20.37 Q-100 40,30 Q-150 37.20 32.32 15.25 25.15 0.0 Where player R's payoff is written first. What is the equilibrium in the game? Select one: a. In equilibrium, both firms choose Q = 50. b. There are two equilibria, associated with the (40,30) payoff and the (30,40) payoff. c. The only equilibrium is in mixed strategies. d. In equilibrium, both firms choose Q = 100.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

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Consider the game below: Player R Player C Q-50 Q-100 Q-150 Q-50 37.37 30, 40 20,37 Q-100 40,30 32,32 15.25 Q-150 37,20 25.15 0.0 Where player R's payoff is written first. What is the equilibrium in the game? Select one: O a. In equilibrium, both firms choose Q = 50. b. There are two equilibria, associated with the (40,30) payoff and the (30,40) payoff. The only equilibrium is in mixed strategies. O d. In equilibrium, both firms choose Q = 100.
Consider the game below: Player C Q-50 Q-100 Q=150 Player R Q-50 37.37 30, 40 20,37 Q=100 40,30 32.32 15.25 Q-150 37.20 25.15 0.0 Where player R's payoff is written first. What is the equilibrium in the game? Select one: a. In equilibrium, both firms choose Q = 50. b. There are two equilibria, associated with the (40,30) payoff and the (30,40) payoff. ○ c. The only equilibrium is in mixed strategies. d. In equilibrium, both firms choose Q = 100.
on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.
Little Kona is a small coffee company that is considering entering a market dominated by Big Brew. Each company’s profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price:a. Does either player in this game have a dominant strategy?b. Does your answer to part (a) help you figure out what the other player should do?c. What is the Nash equilibrium? Is there only one?d. Big Brew threatens Little Kona by saying, “If you enter, we’re going to set a low price, so you had better stay out.” Do you think Little Kona should believe the threat? Why or why not?c. If the two firms could collude and agree on how to split the total profits, what outcome would they pick?
Budweiser Medium High 90, 70 60, 50 Low 120, 90 100, 70 Low 115, 100 Miller Medium 130, 60 High 90, 20 120, 40 100, 80 Numbers in each cell are profits from the size of an advertising budget- Miller first (in bold), then Budweiser. Two beer companies face the payoff table above for choosing an advertising budget. Does this decision problem have a Nash equilibrium? If so, what is it? Select one: O a. Yes. Low for Miller , Low for Budweiser. O b. No. There is no Nash equilibrium. O c. Yes. Low for Miller, Medium for Budweiser. O d. Yes. High for Miller, High for Budweiser.
Answer all questions, show all working. Consider the following game in strategic or normal form. A2 B2 C2 A1 1,0 1,2 -2,1 B1 6,2 0,3 2,3 C1 2,2 -2,1 2,3 Use the iterative elimination of strictly dominated strategies to reduce the game as much as possible. What is the set of rationalizable strategies for each player? What is/are Nash equilibrium(s) in this game? Explain the differences between cooperative and non- cooperative games. What are the fundamental hypotheses about the behavior of the persons in Game theory?
Little Kona is a small coffee company that is considering entering a market dominated by Big Brew. Each company's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price: True or False: Only Little Kona has a dominant strategy in this game. True or False Which of the following outcomes represent a Nash equilibrium in this case? Check all that apply. Big Brew maintains a high price and Little Kona enters. a.Big Brew maintains a low price and Little Kona enters. b.Big Brew maintains a high price and Little Kona does not enter. c.Big Brew maintains a low price and Little Kona does not enter. Big Brew threatens Little Kona by saying, “If you enter, we're going to set a low price, so you had better stay out.” True or False: Little Kona should not believe the threat. True or False If the two firms could collude and agree on how to split the total profits, what outcome would they…
Please no written by hand and no image (Bertrand's duopoly game with discrete prices) Consider the variant of the example of Bertrand's duopoly game in this section in which each firm is restricted to choose a price that is an integral number of cents. Take the monetary unit to be a cent, and assume that c is an integer and a>c+!. Is (c,c) a nash equilibrium of this game? Is there any other nash equilibrium?
on Mary, UE, BD UF, AC DF, BC UF, BD DE, AC DE, BC Nancy U D Nancy -5,4 Mary -0,2 -6,2 -2.6 Which of the following answers is a subgame perfect Nash equilibrium in this game? Check all that apply. (Answers below are formatted as Mary's strategy, Nancy's strategy.)
Consider the following game: ● ● U P1 M D P2 C R L 1, 24, 36, 5 1,5 2,7 4, 3 2, 43, 25, 2 Identify the undominated strategies of P1 and P2. Which strategies are rationalizable? Find all the Nash equilibrium of this game. Illustrate your answer by a clearly labelled best response graph, with P1's strategy on the x-axis and P2's strategy on the y-axis.
L 0 4 15.1 X₂ A M R 0 1 4 0 2 B L 4 0 с X3 M R 0 1 3 FIGURE 15.5 Exercise 15.1. Equilibrium Selection: Consider the extensive-form game in Figure 15.5. a. Find all the Bayesian Nash equilibria of this game. b. Which of the Bayesian Nash equilibria are also perfect Bayesian equi- libria? Why?
9. Little Kona is a small coffee company that is consider- ing entering a market dominated by Big Brew. Each company's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price: Little Kona Enter Don't Enter High Price Kona makes $2 million Kona makes zero Big Brew Brew makes $3 million Brew makes $7 million Kona loses $1 million Low Price Kona makes zero Brew makes $1 million Brew makes $2 million