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 |
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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