Question

Find all pure strategy Nash Equilibria in the following games

a.)    Player 2

	b1	b2	b3
a1	1,3	2,2	1,2
a2	2,3	2,3	2,1
a3	1,1	1,2	3,2
a4	1,2	3,1	2,3

Player 1

b.) Player 2

	A	B	C	D
A	1,3	3,1	0,2	1,1
B	1,2	1,2	2,3	1,1
C	3,2	2,1	1,3	0,3
D	2,0	3,0	1,1	2,2

Player 1

c.) Player 2

	S	B
S	3,2	1,1
B	0,0	2,3

Answer 1

Ans.(a)There are 2 pure strategy nash equilibria in this game : (a2,b1) and (a3,b3).

If player 1 chooses a2 ,player 2 will get maximimum payoff by choosing b1 and b2. But note that at (a2,b2) player 1 has an incentive to switch strategy to a4 in order to get a higher payoff.So, (a2,b2) is not nash equilibrium.And at (a2,b1) no player has any incentive to switch to some other strategy .So, (a2,b1) is nash equilibrium.Similarly , at (a3,b3) no player has any incentive to switch to some other strategy .So, (a3,b3) is nash equilibrium.

Ans.(B) There are 2 pure strategy nash equilibria in this game : (B,C) and (D,D).

If player 1 chooses B ,player 2 will get maximimum payoff by choosing C. And at (B,C) no player has any incentive to switch to some other strategy .So, (B,C) is a nash equilibrium.Similarly, (D,D) is a nash equilibrium.

Ans.(c) There are 2 pure strategy nash equilibria in this game : (S,S) and (B,B).

If player 1 chooses S ,player 2 will get maximimum payoff by choosing S. And at (S,S) no player has any incentive to switch to some other strategy .So, (S,S) is a nash equilibrium.Similarly,(B,B) is a nash equilibrium.

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