Libertyville has two optometrists, Dr. Smith (S) and Dr. Jones (S). Each optomet

Question

Libertyville has two optometrists, Dr. Smith (S) and Dr. Jones (S). Each optometrist can choose to advertise his service or not. The net revenue to each optometrist, in thousands of dollars, is listed on the payoff matrix below. Answer questions a through c:

a. [10 points] Does Dr. Smith have a dominant strategy?

b. [10 points] Does Dr. Jones have a dominant strategy?

c. [ 5 points] Does a Nash equilibrium exist for this game?

                                                                          Dr. Smith (S)   

                                                       Advertise                    Don’t advertise

                              Advertise            S: $383                         S: $384

Dr. Jones (J)                                   J: $373                       J: $413
           
                         Don’t advertise        S: $423                      J: $363
                                                         S: $403                     J: $393

(Above is chart for problem)

Explanation / Answer

Answer:

a. Does Dr. Smith have a dominant strategy?

Yes, if both of them advertise as well as Smith only advertises, he has a dominant strategy.

b. Does Dr. Jones have a dominant strategy?

Yes, if both of them don’t advertise as well as Jones only advertises, he has a dominant strategy.

c. Does Nash equilibrium exist for this game?

No, the game does not exist a Nash equilibrium neither advertises nor don’t advertise of both of the optometrists.

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