Burger King and Wendys are engaging into the following onesh

Burger King and Wendy’s are engaging into the following one-shot game: if Burger King advertises and Wendy’s does not, Burger King will make $20 million in profits and Wendy’s will make $6 million. If Wendy’s advertises and Burger King does not, Burger King will make $2 million and Wendy’s will make $6 million. If Burger King advertises and Wendy’s advertises, each firm earns $10 million. If neither firm advertises, Wendy’s will make $8 million and Burger King will make $4 million.

(a) Write the payoff matrix for the above game.

(b) Does Burger King have a dominant strategy?

(c) Does Wendy’s have a dominant strategy?

(d) What is the Nash equilibrium for the one-shot game?

Solution

pay off :- Wendy

NA A

Burger King NA ,4,8 2,6

A 20,6 10,10

yes Wendy has a dominant strategy ie when it chooses not advertising even if burger king advertises or do not advertises its pay off is more than that of burger king\'s pay off.

Nash equilibrium is that condition from where both the parties have no incentive to deviate. Here (A,A) is nash equilibirum