Question

Martha and Don are competitors in a local market and each is trying to decide if it is worthwhile to advertise. If both of them advertise, each will earn a profit of $5000. If neither of them advertises, each will earn a profit of $10 000. If one advertises and the other doesn't, then the one who advertises will earn a profit of $15 000 and the other will earn $7000. What is Martha’s dominant strategy?

a. She should advertise, and she will earn $5000.
b. She should not advertise, and she will earn $10 000.
c. Martha has no strategy that guarantees her the most money.
d. She should advertise, and she will earn $15 000.

Answer 1

For this , first we will form a table of the dominant strategies

Don  

martha

	Advertise	Dont advertise
Advertise	5000,5000	15000,7000
Dont advertise	7000,15000	10000,10000

The rows are of player 1 ie Martha and columns of player 2

Now for dominant strategy is the one which the player chooses irrespective of the strategy the other player chooses

Here when Don chooses to advertise , Martha will not advertise since her payoff then is more than when she advertises.

Similarly when Don chooses to not advertise, Mrtha will choose to advertise since her payoff is more when she advertises.

So in both the cases , her strategy is dependent on Don's strategy,

So in this case she doesnt have a dominant strategy because she advertises when Don doesn't and does not advertise when Don does.

So answer is option C)  Martha has no strategy that guarantees her the most money.

(you can comment for doubts )