Suppose that Proton and Meek are the two leading firms in their sports drink ind

Question

Suppose that Proton and Meek are the two leading firms in their sports drink industry and that their respetive annual profits depends not only one their advertising decisions but also on their rival's advertising decisions as well. The effect of these decisions is captured in the payoff estimates below:

If both firms advertis, Proton profits would be $100 mil and Meek profits would be $85 mil. If neither firms advertise, profits would be $120 mil for Proton and $100 mil for Meek. If Proton does advertise and Meek does not, profit would be $150 mil for Proton and $65 mil for Meek. Meek advertisd and Proton dont, Meek makes $115 mil and Proton makes $75 mil.

1.Present this problem in the form of Game Theory Matrix
2. What is the dominant strategy. if and for Proton? For Meek, if it exist?
3. What would the profits for each company be under a Nash Equilibrium solution, if exist?

Explanation / Answer

Question 1

Following is the Game Theory Matrix -

Proton

Meek

Advertise

Do not advertise

Advertise

$100 million, $85 million

$150 million, $65 million

Do not advertise

$75 million, $115 million

$120 million, $100 million

Question 2

If Meek advertises, Proton will also advertise as pay-off is greater for Proton in that case.

If Meek do not advertises, Proton will still advertise as pay-off is greater for Proton in that case.

So, whatever be the strategy adopted by Meek, Proton will always choose to advertise.

Thus, the dominant strategy for Proton is to advertise.

If Proton advertises, Meek will also advertise as pay-off is greater for Meek in that case.

If Proton do not advertises, Meek will still advertise as pay-off is greater for Meek in that case.

So, whatever be the strategy adopted by Proton, Meek will always choose to advertise.

Thus, the dominant strategy for Meek is to advertise.

Question 3

The combination of dominant strategies is the Nash equilibrium of the game.

So, the Nash equilibrium of this game is both firms will advertise.

In this solution, Proton will earn $100 million as profit while Meek will earn $85 million as profit.

Proton

Meek

Advertise

Do not advertise

Advertise

$100 million, $85 million

$150 million, $65 million

Do not advertise

$75 million, $115 million

$120 million, $100 million

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