12. Pat’s and Geno’s are two rival cheesesteak restaurants in Philadelphia, Pennsylvania, that are located across the street from each other. Since they serve almost the same food, they are fiercely competitive. With the weather in Philly improving, sales at both firms are expected to increase over the next few months. Suppose both firms are now considering expanding their menu to include cheesecake and other desserts to boost sales further. The payoffs are given in the following table:

a. Suppose Geno’s and Pat’s make their decisions simultaneously. What is the Nash equilibrium in this game?

b. Now suppose that Pat’s will decide whether or not to introduce desserts and then Geno’s will decide. Draw the game tree for this extensive-form game.

c. Use backward induction to determine how the extensive-form version of this game will be played.