(10 total points) Suppose that two players are playing the following game. Playe

Question

(10 total points) Suppose that two players are playing the following game. Player A can choose either Top or Bottom, and Player B can choose either Left or Right. The payoffs are given in the following table: Player B LEFT RIGHT Top 4 5 1 4 Player A Bottom 5 1 3 8 where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B. A) (1 point) Does player A have a dominant strategy, and if so what is it? B) (1 point) Does player B have a dominant strategy and if so what is it? C) (4 points) For each of the following say True if the strategy combination is a Nash equilibrium, and False if it is not a Nash equilibrium: i) Player A plays Top and Player B plays Left ii) Player A plays Bottom and Player B plays Left iii) Player A plays Top and Player B plays Right iv) Player A plays Bottom and Player B plays Right D) (2 points) If each player plays her maximin strategy what will be the outcome of the game? (Give your answer in terms of the strategies each player chooses

Explanation / Answer

5,5 4,6 3,4 6,2 A) Does player A have a dominant strategy, and if so what is it? No B) Does player B have a dominant strategy and if so what is it? Yes, right C) For each of the following say True if the strategy combination is a Nash equilibrium, and False if it is not a Nash equilibrium: i) Player A plays Top and Player B plays Left False ii) Player A plays Bottom and Player B plays Left False iii) Player A plays Top and Player B plays Right True iv) Player A plays Bottom and Player B plays Right True D) If each player plays her maximin strategy what will be the outcome of the game? (Give your answer in terms of the strategies each player chooses) There is no NE but the mixed strategy is depends on who plays first. Player 2 will always choose right and player 1 will choose bottom if he goes first and top if second

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