Libertyville has two optometrists Dr Smith S and Dr Jones S

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. Does Dr. Smith have a dominant strategy? b. Does Dr. Jones have a dominant strategy? c. Does a Nash equilibrium exist for this game?

Solution

Let us organise the game as follows

The left side payoffs in any cell are that of the Dr Jones and the right side payoffs in any cells is that of Dr Smith.

a)Dr Smith doesnot have any dominant strategy.If Dr Jones chooses Advertise,Dr Smith will choose Dont Advertise (384>383) and if Dr Jones chooses Dont Advertise, Dr Smith will choose advertise(423>403). THus there is no dominant strategy.

b) In case of Dr Jones, the dominant strategy is advertise as in both the cases where Dr Smith chooses advertise and Dont advertise, Jones will choose to advertise. This is because 373>363 and 413>393.

c)The Nash equilibrium is Jones choose advertise and Smith choose dont advertise as that is boths best response.

	Advertise	Dont Advertise
Advertise	373,383	413,384
Dont Advertise	363,423	393,403