Question

Firm B                      

                                                          Strategy 1        Strategy 2

                                                                          

                                     Strategy 1: 28, 28 15, 35                        

                  Firm A                                                     

                                    Strategy 2: 35, 15 20, 20                                    

                                                

            2. (2 pts.) Does Firm A have a dominant strategy? _______If yes, which strategy? _________

                                                                           (yes or no)

            3. (2 pts.) Does Firm B have a dominant strategy? _______If so, which strategy? _________

                                                                           (yes or no)    

                        

4. (2 pts.) Are there any Nash equilibria? If there are any Nash equilibria, identify any and all of them.

_____________________________________________________________________                  

Answer 1

(2) Yes.

A dominant strategy is a strategy chosen by one player irrespective of the strategy chosen by the other player.

Firm A will choose Strategy 2 irrespective of strategy chosen by Firm B since payoff is higher (35 > 28 & 20 > 15). So Strategy 2 is Firm A's dominant strategy.

(3) Yes.

A dominant strategy is a strategy chosen by one player irrespective of the strategy chosen by the other player.

Firm B will choose Strategy 2 irrespective of strategy chosen by Firm A since payoff is higher (35 > 28 & 20 > 15). So Strategy 2 is Firm B's dominant strategy.

(3) Nash equilibrium is: (Strategy 2, Strategy 2)

When Firm B chooses Strategy 1, Firm A's best strategy is Strategy 2 since payoff is higher (35 > 28).

When Firm B chooses Strategy 2, Firm A's best strategy is Strategy 2 since payoff is higher (20 > 15).

When Firm A chooses Strategy 1, Firm B's best strategy is Strategy 2 since payoff is higher (35 > 28).

When Firm A chooses Strategy 2, Firm B's best strategy is Strategy 2 since payoff is higher (20 > 15).

Therefore, Nash equilibrium is: (Strategy 2, Strategy 2) [See below].