In a one shot game, if you advertise and your rival advertise, you can each earn

Question

In a one shot game, if you advertise and your rival advertise, you can each earn $5 million in profits. If either of you advertises, you 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 you rival will make $3 million. If your rival advertises and you do not, you will make$1 million and you rival will make $3 million.

a. Write the above game in normal form?

b. Identify any dominant strategy that you have?

c. Identify and dominant strategy your rival has?

d. What is the Nash equilibrium for the one shot game?

e. If you were the type of manage that would be inclined to offer a bribe to your rival to not advertise, what is the most you are willing to offer?

Explanation / Answer

a)

b)

My dominant strategy is to advertise, as i can earn a profit of $5 if i advertise and $1 profit if i don't advertise

c)

Rival's dominant strategy is to advertise, as it can earn a profit of $5 if it advertises and $3 profit if it does not advertise

d)

Nash equilibrium for the one shot game is both to advertise i.e (5,5), as they try to adapt their dominant strategies

e)

I would offer a bribe of $2 as this would provide rival with the maximum profit i.e. $5 which it would get if it advertises. Then my net payoff would be $10-$2 =$8, rival pay off would be $3 + $2 =$5 , which would be win-win situation for both

you your rival Rival Advertise Rival Does not Advertise You Advertise (5,5) (10,3) You don't Advertise (1, 3) (2,4)

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