Question

QUESTTON 4 Player Il E D A 3,34,21,4 B 2,0 3,0-1,1 с 1,1 2,1 0,2 Player Consider the game above. Select all that apply. a Strategy B weakly dominates C. Strategy D weakly dominates E. c. The game does not have a dominant strategy solution. d. F is a dominant strategy. e. (A,D) is the dominant strategy solution.

Answer 1

a game is a strategic interaction between economic agents trying to make an economic decision. The agents who tried to make a decision considering the decision of others is called player. Each player has finite choices to decide upon, these are called the strategies. Each strategy corresponds to a definite outcome, called the payoff. Now, these payoff is subject to the decision of other players as well. The strategy which corresponds to the highest outcome is called the dominant strategy, all other strategies are dominated by this dominant strategy. The weakly dominated strategy is one whose payoffs are at least as good as the payoff of another strategy.

In this game,

• $S_D\left \{ 3, 0, 1 \right \}\succeq S_E\left \{ 2, 0, -1 \right \}$
• A is the dominant strategy of player 1
• F is the dominant strategy of player 2

To determine if the game has a dominant strategy following steps are followed:

1. Underline the response of player 1 given the strategy of player 2 each at a time. This is done in the figure below, the player always chooses A no matter what 2 choose.
2. The same is followed for player 2 as well. In this case player 2 always plays F.
3. Then A and F is the dominant strategies of respective players.

Therefore, the correct options are: (b), (d)