In a one-shot game, if you advertise and your rival advertises, you will each earn $5...

In a one-shot game, if you advertise and your rival advertises, you will each earn $5 million in profits. If neither of you advertises, your rival will make $4 million and you will make $2 million. If you advertise and your rival does not, you will make $10 million and your rival will make $3 million. If your rival advertises and you do not, you will make $1 million and your rival will make $3 million.

a. Write the above game in normal form.

b. Do you have a dominant strategy?

c. Does your rival have a dominant strategy?

d. How much would you be willing to bribe your rival not to advertise?

Solutions

Expert Solution

Answer

Part a)

Firm 2 (Rival)

Advertise Don't Advertise

Firm 1 Advertise 5,5 10,3

Don't Advertise 1,3 2,4

Part b)

Yes, Firm 1 (me) has a Dominant Strategy. The dominant strategy is to Advertise as Firm 1 will be either esrning $5 million or $10 million dpending on Firm 2's strategy. However, these payofffs will be anyway higher than payoffs if Firm 1 does not advertise.

Part c)

No, Firm 2 (rival firm) does not have a dominant strategy as it will choose to Advertise (payoff = $5 million) only if Firm 1 is advertising and will not choose to advertise (payoff = $4 million) when Firm 1 is not advertising. Thus, the strategy of Firm 2 is dependent on the strategy chosen by Firm 1.

Part d): $5 million

If the rival firm (Firm 2) does not Advertise, it will earn $3 million as Firm 1 is surely going to Advertise. Thus, $2 million needs to be given to this Firm 2 so that its payoff becomes $5 million such that it now becomes indifferent between advertising and not advertising. (as it will be earning $5 million now in both the cases)

Rahul Sunny answered 1 year ago

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