Question

Q. 1. Consider the following pay off matrix of the two players; A and B. What are the Nash equilibria in the game?                                                                                         

Player 2
		Strategy D	Strategy E	Strategy F
Player 1	Strategy A	4, 2	13, 6	1, 3
	Strategy B	11, 2	0, 0	15, 10
	Strategy C	12, 14	4, 11	5, 4

Answer 1

Player 2 Strategy D Strategy E Strategy F Player 1 Strategy A 4, 2 13, 6 1, 3 Strategy B 11, 2 0, 0 15, 10 Strategy C 12, 14 4, 11 5, 4

A strategy is said to be dominant if, the pay off the strategy is largest among the available strategy to this players regardless of strategy chosen by other players. Hence, it can be said that a strategy is dominant if it is always superior, compare to any other strategy, for any profile of other player’s action

Since the Nash equilibrium occurs when every player wants to choose the best possible strategy, given the strategies of another player. Once the Nash equilibrium is reached, there is no incentive to change the strategy by the both players.

A strategy is said to be dominant if, the pay off the strategy is largest among the available strategy to this players regardless of strategy chosen by other players. Hence, it can be said that a strategy is dominant if it is always superior, compare to any other strategy, for any profile of other player’s action

Since the Nash equilibrium occurs when every player wants to choose the best possible strategy, given the strategies of another player. Once the Nash equilibrium is reached, there is no incentive to change the strategy by the both players.

As it can be seen in the game, that Player 1 chooses strategy C given the D strategy chosen by Player 2.(12)

As it can be seen in the game, that Player 1 chooses strategy A given the E strategy chosen by Player 2.(13)

As it can be seen in the game, that Player 1 chooses strategy B given the F strategy chosen by Player 2.(15)

As it can be seen in the game, that Player 2 chooses strategy E given the A strategy chosen by Player 1.(6)

As it can be seen in the game, that Player 2 chooses strategy F given the B strategy chosen by Player 1.(10)

As it can be seen in the game, that Player 2 chooses strategy D given the C strategy chosen by Player 1.(14)

Since both player 1 and 2 have dominant strategy in (Strategy B and Strategy F) (15 and 10).

Hence Nash equilibrium is (Strategy B and Strategy F) (15 and 10).