Question 3: [5pt total] Consider the following game: Player 1 Player 2 X Y Z A...

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Question 3: [5pt total] Consider the following game: Player 1 Player 2 X Y Z A 4,0 -3,8 -7, -1 B-4,3 0,6 9,5 C3,2 2,-1 11, 9

Answer 1

Answer #1

1. For player 1, if player 2 plays X, the best response is to play A with the maximum payoff of 4

2. For player 2, if player 1 plays B, the best response is to play Y with the maximum payoff of 6

3. Social welfare maximum:

This is the condition when the total payoffs for Player 1 and 2 is maximum which is the case

when Player 1 plays C and Player 2 plays Z with total payoff of 20

4. Dominant strategies for Player 1

For player 1, one dominant strategy is to play C over B since the payoff is always higher than that of playing B

5. For nash equilibrium

When Player 2 plays X, 1 plays A, when player 2 plays Y, 1 plays C, when plays 2 player Z, 1 plays C

When player 1 plays A, 2 plays Y, when player 1 plays B, 2 plays Y, when player 1 plays C, 2 plays Z

The plays by player 1 and 2 are highlighted in bold below:

As can be seeon on the case C,Z has both bolds that implies this being the nash equilibrium

Answer 2

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