Suppose that two players are playing the following game. Player 1 can choose eit
ID: 1222091 • Letter: S
Question
Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table: where the number on the left is the payoff to Player 1, and the number on the right is the payoff to Player 2. A) Does Player 1 have a dominant strategy, and if so what is it? B) Does Player 2 have a dominant strategy and if so what is it? C) For each of the following strategy combinations, write TRUE if it is a Nash Equilibrium, and FALSE if it is not: i) Top/Left ii) Top/Right iii) Bottom/Left iv) Bottom Right D) What is Player 1's maximin strategy? E) What is Player 2's maximin strategy? F) If the game were played with Player 1 moving first and Player 2 moving second, using the backward induction method we went over in class, what strategy will each player choose?Explanation / Answer
a. Yes, player 1 has a dominant strategy. Comparing pay offs 6 with 2 and 9 with 5, we see that the pay offs are higher in both the cases when player 1 chooses TOP.
Thus, the dominant strategy of player 1 is TOP.
b. Comparing 1 with 4 and 4 with 3, we see that player 2 does not have any dominant strategy.
c. The Nash equilibrium of the game is (9,4). This is because when player 1 chooses Top, the best strategy for paler 2 is to choose Right. When player 2 chooses Bottom, the best strategy for player 1 is to choose top.
Thus, Top, Bottom is the Nash equilibrium of the game.
d. The minimum of 6 and 2 is 2 and minimum of 9 and 5 is 5. The maximum of 2 and 5 is 5. SO, max min strategy of payer 1 is Bottom.
e. The minimum of 1 and 4 is 1 and minimum of 4 and 3 is 3. The maximum of 1 and 3 is 3. So, max min strategy of player 2 is Right.
f.
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