Question

Consider the hypothetical example using game theory. Assume that it is a one-off simultaneous move game, and that each player only cares about their own payoff.

LG and Samsung are deciding whether or not to release a new 360-degree camera.

If both LG and Samsung release the camera, then LG will make $20 million profit, and Samsung will make $40 million profit.

If LG releases the camera, and Samsung does not, then LG will make $30 million profit and Samsung will make $0 profit.

If LG does not release the camera, and Samsung does, then LG will make $30 million profit, and Samsung will make $60 million profit.

If neither LG nor Samsung release the camera, they both receive $0 profit

a) Depict the above outcomes in a payoff matrix

b) If LG releases the camera, what is Samsung’s best response?

c) Does LG have a dominant strategy? If so, what is it? If not, explain why not.

d) Does Samsung have a dominant strategy? If so, what is it? If not, explain why not.

e) Find the Nash Equilibrium of the game.

f) Explain why the Nash Equilibrium is a likely outcome for this game.

Answer 1

a) The payoff matrix would be,

		Samsung	Samsung
		Release	Do not release
LG	Release	$20 million, $40 million	$30 million, $0 million
LG	Do not release	$30 million, $60 million	$0 million, $0 million

b) If LG chooses to release the camera, Samsung will also choose to release the camera as it will have a higher payoff of $40 million by doing so.

c) If Samsung chooses to release the camera, LG would choose to not release the camera and if Samsung chooses not to release the camera, LG would choose to release the camera. Thus, we can see that LG does not have a dominant strategy.

d) If LG chooses to release the camera, Samsung would choose to release the camera and if LG  chooses not to release the camera, Samsung would again choose to release the camera. Thus, we can see that Samsung has a dominant strategy of releasing the camera.

e) We know that irrespective of LG’s decision, Samsung will always choose to release the camera. Now, when Samsung chooses to release the camera, LG would choose not to release the camera. Hence, we can see that the Nash Equilibrium is (Do not release, Release), which means that LG will choose not to release the camera and Samsung would choose to release the camera. By doing so, payoff for LG would be $30 million and the payoff for Samsung would be $60 million.

f) Nash Equilibrium is the likely outcome for this game, as no company would like to deviate from these strategies unless the other company does so. Secondly, both the companies are getting the maximum possible payoffs by using these strategies.

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