EBK MICROECONOMICS
2nd Edition
ISBN: 8220103679701
Author: List
Publisher: YUZU
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Question
Chapter 13, Problem 4P
(a)
To determine
Existence of a dominant strategy for the players.
(b)
To determine
Nash equilibria of the asymmetric game.
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We consider the following three-player strategic form game, where Alice's strategies are U, C, and D, and Bob's strategies are L, M, and R, and Carol's strategies are A and B. Carol's strategy consists of choosing which table will be used for the payoffs, Table A or Table B.Table A is below, where for each cell the first number is Alice's payoff, the second number is Bob's payoff and the third number is Carol's payoff..
L
M
R
U
8,11,14
3,13,9
0,5,8
C
9,9,8
8,7,7
6,5,7
D
0,8,12
4,9,2
0,4,8
Table A
Table B is below, where again, for each cell, the first number is Alice's payoff, the second number is Bob's payoff and the third number is Carol's payoff..
L
M
R
U
14,1,0
13,2,11
1,3,2
C
0,0,2
7,2,3
14,3,2
D
7,12,11
12,12,0
2,11,2
Table B
This game may not have any Nash equilibrium in pure strategies, or it may have one or more equilibria.How many Nash equilibria does this game have?
Refer to the normal-form game of price competition in the payoff matrix below
Firm B
Low Price
High Price
Firm A
Low Price
0, 0
50, −10
High Price
−10, 50
20, 20
Suppose the game is infinitely repeated, and the interest rate is 20 percent. Both firms agree to charge a high price, provided no player has charged a low price in the past. This collusive outcome will be implemented with a trigger strategy that states that if any firm cheats, then the agreement is no longer valid, and each firm may make independent decisions. Will the trigger strategy be effective in implementing the collusive agreement? Please explain and show all necessary calculations.
Use the following normal-form game to answer the following questions. a. For what values of x is strategy D (strictly) dominant for player 2? b. For what values of x is strategy B (strictly) dominant for player 1? c. For what values of x is (B, D) the only Nash equilibrium of the game?
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Similar questions
- Consider the payoff matrix of a two player game below what are the strategies in the Nash equilibriumarrow_forwardConsider the following game. There are two companies that sell Haitian coffee. Each company currently makes$5 million in revenue. They need to determine whether they should engage in a social media advertising campaign. Advertising costs$2 million for each company. If one company advertises, and the other does not, then the one that advertises captures$3 million from the company that does not. If both companies advertise, they gain nothing. Draw the payoff matrix. What is this game’s Nash equilibrium (or equilibria)arrow_forwardConsider the following entry-deterrence game. A potential entrant has two strategies, “Enter” or “Stay Out”. An incumbent firm can either Price Low or Price High, depending on whether they want to try to fight or accommodate the entrant. (The Price Low option could be a limit price, for example). Suppose if the entrant Enters and the incumbent Prices Low, both firms lose $-1M. If the entrant enters and the incumbent Prices High, each firm earns $2M. If the Entrant doesn’t enter, the incumbent earns $4M and the entrant earns $0. a)Using the concept of Nash Equilibrium, what are the predicted strategies and profits? Set up a game box or tree and explain your reasoning. b) Give an example of a different profit outcome that would lead to a different Nash Equilibrium. (From this, you can see that sometimes deterrence is effective and sometimes it isn’t, depending on the profits).arrow_forward
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