28 Player 1 has three strategies (I, II, III) and player 2 has three strategies

Question

28 Player 1 has three strategies (I, II, III) and player 2 has three strategies (A, B, C). Given the following payoff matrix (the bigger number, the better; the first number of each pair is for player 1.) Player 2 Strategy 12, 12 20, 1 15, -1 1,20 6, 6 9, 0 1, 15 0, 9 2, 2 Player 1 a. both players have a dominant strategy none ofthe playershas a dominantstrategy. player 1 has a dominant strategy while player 2 does not. player 2 has a dominant strategy while player 1 does not. c. d. Based on the above information (in question 28), we conclude that a. the Nash equilibrium payoff would be (12, 12) b. the Nash equilibrium payoff would be (6, 6) d) the Nash equilibrium payoffwould be (2,2). 29 there is no Nash equilibrium. Player 1 has two strategies (1, II) and player 2 has two strategies (A, B). Given the following payoff matrix (the bigger number, the better, the first number of each pair is for player 1.) 30 Player 2 Strategy 25, 15 30, 0 15, 20 40, 5 Player 1 a. both players have a dominant strategy none of the players has a dominant strategy. player 1 has a dominant strategy while player 2 does not. c. d. player 2 has a dominant strategy while player 1 does not. Based on the above information (in question 30), we conclude that a the Nash equilibrium payoff would be (25, 15). the Nash equilibrium payoff would be (30, 0). 31 c. the Nash equilibrium payoff would be (15, 20) d. the Nash equilibrium payoff would be (40, 5).

Explanation / Answer

28) B. No player have dominant startegy because dominant strategy is a strategy which a player playes irrespective of what other player plays. Player 1 plays 1 if player 2 plays A and plays second if player 2 plays B. Thus player 1 strategy changes which makes that player 1 dont have dominant strategy. Similarly player 2 also dont have any dominant strategy

29)C. Nash equilibrium is a strategy set where no player have any incentive to change their strategy given the other player strategy.

30)ans is D

Player 2 has dominant strategy because player 2 plays A whatever the player 1 plays.

31) A

(1,A) is a nash equilibrium and payoff is (25,15)

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