EBK MICROECONOMICS
EBK MICROECONOMICS
2nd Edition
ISBN: 8220103679701
Author: List
Publisher: YUZU
Question
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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outcome will be implemented with a trigger strategy that states that if any firm cheats, then the agreement is no longer valid, and each firm may make independent decisions.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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