Micro Theory Extra Credit Assignment Due at the beginning of class on Friday, De

Question

Micro Theory Extra Credit Assignment Due at the beginning of class on Friday, December glh. No late assignments will be accepted! Each question is worth one percentage point applied to your final exam. (6 percentage points total are possible.) Remember a Nash Equilibrium is stated in terms of strategies, not payoffs! 1. Consider the following 2 player simultaneous game Player 2 Player 1 A 5,1 2,4 3,2 3,3 a) b) c) Does player 1 have a dominant strategy? Does player 2 have a dominant strategy? Find the Nash Equilibrium of this game. 2. Consider the following 2 player simultaneous game: Player 2 Player 1 A 2,2 a) b) c) Does player 1 have a dominant strategy? Does player 2 have a dominant strategy? Find the Nash Equilibrium of this game. 3. Consider the following 2 player simultaneous game: Player 2 Player 1 A 3,5 0,6 4.0 1,1 a) Does player 1 have a dominant strategy? b) Does player 2 have a dominant strategy? c) Find the Nash Equilibrium of this game.

Explanation / Answer

1. a) Dominant strategy is a strategy for a player i.e. best response to all strategy profile of other player. If all players in a game have a dominant strategy then we say that Game has dominant strategy equilibrium.

Player 1 does not have dominant strategy because his payoff depends upon the decision of Player 2.

b) Player 2 has the dominant strategy of choosing D because his payoff is greater irrespective of decision of Player 1.

c) Nash equilibrium is a strategy profile such that for each player given strategy, it is best response. Nash equilibrium is a set of strategies such that each player is doing their best given the strategy of other player.

If Player 1 chooses A then best response of Player 2 is to choose D.

If Player 2 chooses D then best response of Player 1 is to choose B.

So, (A; D) is not the nash equilibrium.

If Player 1 chooses B then best response of Player 2 is to choose D.

If Player 2 chooses D then best response of Player 1 is to choose B.

So, (B; D) is the nash equilibrium.

2. a) No, Player 1 does not have dominant strategy.

b) No, Player 2 does not have dominant strategy.

c) If Player 1 chooses A then best response of Player 2 is to choose C.

If Player 2 chooses C then best response of Player 1 is to choose B.

So, (A; C) is not the nash equilibrium.

If Player 1 chooses B then best response of Player 2 is to choose D.

If Player 2 chooses D then best response of Player 1 is to choose A.

So, (B; D) is not the nash equilibrium.

3. a) Player 1 has dominant strategy of B.

b) Player 2 has dominant strategy of D.

c) If Player 1 chooses A then best response of Player 2 is to choose D.

If Player 2 chooses D then best response of Player 1 is to choose B.

So, (A; D) is not the nash equilibrium.

If Player 1 chooses B then best response of Player 2 is to choose D.

If Player 2 chooses D then best response of Player 1 is to choose B.

So, (B; D) is the nash equilibrium.

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