Question

Two grocery stores compete against each other in a community. Both are considering an increase in advertising expenditures. Their interdependent alternatives are described by the payoff matrix below (first entry is for firm 1).                                                                                         Firm 2
Advertise				Don’t Advertise
Firm 1	Advertise		(6, 4)			(9, 5)
Don’t Advertise		(3, 7)			(8, 6)

i. Determine whether each firm has a dominant strategy and, if it does, identify the strategy.

Firm 1: _________________________________; Firm 2: _______________________________

ii. Determine the Nash equilibrium

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.

1.

Since Player I has dominant strategy in strategy advertise when Player II chooses strategy advertise. (6)

Player I has dominant strategy in strategy advertise when Player II chooses strategy don't advertise. (9)

Since Player II has dominant strategy in strategy don't advertise when Player I chooses strategy advertise. (5)

Player II has dominant strategy in strategy advertise when Player 2 chooses strategy don't advertise. (7)

2.

Since both player has dominant strategy in ( advertise, don't advertise)= ( 9,5)

Hence this is the nash equilibrium.