Question

11.       In the following game, numbers on the left of the comma are payoffs to A; numbers on the right are payoffs to B. Identify the Nash equilibria, if any.

A/B	B1	B2	B3
A1	5,6	3,5	0,4
A2	6,7	3,9	5,2
A3	7,5	4,4	4,3
A4	3,8	7,2	6,8

Answer 1

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.

Since A has dominant strategy in A3 when B chooses B1. (7)

A has dominant strategy in A4 when B chooses B2. (7)

A has dominant strategy in A4 when B chooses B3. (6)

B has dominant strategy in B1 when A chooses A1. (6)

B has dominant strategy in B2 when A chooses A2. (9)

B has dominant strategy in B1 when A chooses A3. (5)

B has dominant strategy in B1 and B3 when A chooses A4. (8)

Hence 2 nash equilibrium are [ (A3,B1) (7 ,5)] and  [ (A4,B3) (6, 8)]